###### Advertisements

###### Advertisements

Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate

###### Advertisements

#### Solution

Angles are measured in degrees. The symbol for degree is a little circle.

The full circle is 360° (360 degree). A half circle or a straight angle is 180°. A quarter circle or a right angle is 90°.

Place the mid-point of the protractor on the Vertex of the angle. Line up one side of the angle with the Zero line of the protractor (where you see the number 0).

Read the degrees here the other side crosses the number scale.

**1.** Measure the angles.

**2.** Measure the angles. Label each angle as acute or obtuse.

**3.** Tasha measured an acute angle, and got 146°. The teacher pointed out that she had read the wrong set of numbers on the protractor.

**4.** Measure the following angles using your own protractor. If you need to, make the sides of the angles longer with a ruler.

**5.** Draw four dots and connect them so that you get a quadrilateral.

Measure all the angles of your quadrilateral. Then add the angle measure.

#### APPEARS IN

#### RELATED QUESTIONS

In fig., circles C(O, r) and C(O’, r/2) touch internally at a point A and AB is a chord of the circle C (O, r) intersecting C(O’, r/2) at C, Prove that AC = CB.

Fill in the blanks:

A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

Fill in the blank

The angle between tangent at a point on a circle and the radius through the point is ........

Find the length of a tangent drawn to a circle with radius 5cm, from a point 13 cm from the center of the circle.

If the quadrilateral sides touch the circle prove that sum of pair of opposite sides is equal to the sum of other pair.

If ΔABC is isosceles with AB = AC and C (0, 2) is the in circle of the ΔABC touching BC at L, prove that L, bisects BC.

The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4cm,5cm and 7cm respectively. Determine the length of fourth side.

Fill in the blank:

An arc is a ................ when its ends are the ends of a diameter.

true or false

Sector is the region between the chord and its corresponding arc.

In the below fig. O is the centre of the circle. If ∠APB = 50°, find ∠AOB and ∠OAB.

O is the centre of a circle of radius 10 cm. P is any point in the circle such that OP = 6 cm. A is the point travelling along the circumference. x is the distance from A to P. what are the least and the greatest values of x in cm? what is the position of the points O, P and A at these values?

Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm; find the length of another chord.

In the given figure ABC is an isosceles triangle and O is the centre of its circumcircle. Prove that AP bisects angle BPC .

In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30° , prove that BA : AT = 2 : 1.

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the lengths of TP and TQ.

If the difference between the circumference and the radius of a circle is 37 cm, then using`22/7`, the circumference (in cm) of the circle is:

In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?

The circumference of a circle is 22 cm. The area of its quadrant (in cm^{2}) is

A chord of a circle of radius 14 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. `[User pi22/7 and sqrt3=1.73]`

An equilateral triangle *ABC *is inscribed in a circle with centre *O*. The measures of ∠*BOC*is

The greatest chord of a circle is called its

In the given figure, common tangents *PQ* and *RS* to two circles intersect at *A*. Prove that *PQ* = *RS.*

A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of ∆PQR is 336 cm^{2}, find the sides PQ and PR.

*AB* is a chord of a circle with centre *O* , *AOC* is a diameter and *AT* is the tangent at* A* as shown in Fig . 10.70. Prove that \[\angle\]*BAT* = \[\angle\] *ACB*.

In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

Choose correct alternative answer and fill in the blank.

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is .........

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is ______.

The point of concurrence of all angle bisectors of a triangle is called the ______.

The circle which passes through all the vertices of a triangle is called ______.

Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ______.

The length of the longest chord of the circle with radius 2.9 cm is ______.

Radius of a circle with centre O is 4 cm. If l(OP) = 4.2 cm, say where point P will lie.

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is ______.

Find the length of the chord of a circle in the following when:

Radius is 6.5 cm and the distance from the centre is 2.5 cm

In following fig. ABC is an equilateral triangle . A circle is drawn with centre A so that ot cuts AB and AC at M and N respectively. Prove that BN = CM.

In the above figure, `square`XLMT is a rectangle. LM = 21 cm, XL = 10.5 cm. Diameter of the smaller semicircle is half the diameter of the larger semicircle. Find the area of non-shaded region.

In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –

(1) m(arc PR)

(2) m(arc QS)

(3) m(arc QSR)

In the given figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.

**The figure given below shows a circle with center O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm,**

find the radius of the circle.

**In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC at P and OA at Q.**

Prove that:

( i ) ΔOPA ≅ ΔOQC

( ii ) ΔBPC ≅ ΔBQA

**Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points?**

**Suppose you are given a circle. Describe a method by which you can find the center of this circle.**

In an equilateral triangle, prove that the centroid and center of the circum-circle (circumcentre) coincide.

In the given circle with diameter AB, find the value of x.

In the given figure, the area enclosed between the two concentric circles is 770 cm^{2}. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.

If O is the centre of the circle, find the value of x in each of the following figures

**Use the figure given below to fill in the blank:**

Tangent to a circle is _______.

**Use the figure given below to fill in the blank:**

________ is a radius of the circle.

**Use the figure given below to fill in the blank:**

AB is a ______ of the circle.

Draw a circle of radius of 4.2 cm. Mark its center as O. Takes a point A on the circumference of the circle. Join AO and extend it till it meets point B on the circumference of the circle,

(i) Measure the length of AB.

(ii) Assign a special name to AB.

Draw a circle of radius 3.6 cm. In the circle, draw a chord AB = 5 cm. Now shade the minor segment of the circle.

Construct a triangle ABC with AB = 4.2 cm, BC = 6 cm and AC = 5cm. Construct the circumcircle of the triangle drawn.

Construct a triangle PQR with QR = 5.5 cm, ∠Q = 60° and angle R = 45°. Construct the circumcircle cif the triangle PQR.

The diameter of a circle is 12.6 cm. State, the length of its radius.

Can the length of a chord of a circle be greater than its diameter ? Explain.

Draw a circle of diameter 7 cm. Draw two radii of this circle such that the angle between these radii is 90°. Shade the minor sector obtained. Write a special name for this sector.

If the radius of a circle is 5 cm, what will its diameter be?

**Draw circle with the radii given below.**

2 cm

**Draw circle with the radii given below.**

3 cm

**Draw a circle with the radii given below.**

4 cm

Draw a circle of any radius. Show one diameter, one radius, and one chord on that circle.

In the table below, write the names of the points in the interior and exterior of the circle and those on the circle.

Diagram |
Points in the interior of the circle |
Points in the exterior of the circle |
Points on the circle |

The diameter of the circle is 52 cm and the length of one of its chord is 20 cm. Find the distance of the chord from the centre

The chord of length 30 cm is drawn at the distance of 8 cm from the centre of the circle. Find the radius of the circle

Find the length of the chord AC where AB and CD are the two diameters perpendicular to each other of a circle with radius `4sqrt(2)` cm and also find ∠OAC and ∠OCA

A chord is 12 cm away from the centre of the circle of radius 15 cm. Find the length of the chord

In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord

A chord is at a distance of 15 cm from the centre of the circle of radius 25 cm. The length of the chord is

In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is

AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24 cm then the distance of AB from the centre of the circle is

The ratio between the circumference and diameter of any circle is _______

A line segment which joins any two points on a circle is a ___________

The longest chord of a circle is __________

The radius of a circle of diameter 24 cm is _______

A part of circumference of a circle is called as _______

Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) |
diameter (d) |
Circumference (C) |

15 cm |

Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) |
diameter (d) |
Circumference (C) |

1760 cm |

Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) |
diameter (d) |
Circumference (C) |

24 m |

All the radii of a circle are _______________

A line segment joining any point on the circle to its center is called the _____________ of the circle

A line segment with its end points on the circle is called a ______________

Twice the radius is ________________

Find the diameter of the circle

Radius = 10 cm

Find the diameter of the circle

Radius = 8 cm

Find the diameter of the circle

Radius = 6 cm

Find the radius of the circle

Diameter = 24 cm

Find the radius of the circle

Diameter = 30 cm

Find the radius of the circle

Diameter = 76 cm

Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.

A, B, C are any points on the circle with centre O. If m(arc BC) = 110° and m(arc AB) = 125°, find measure arc AC.

In figure, O is the centre of a circle, chord PQ ≅ chord RS. If ∠POR = 70° and (arc RS) = 80°, find

(i) m(arc PR)

(ii) m(arc QS)

(iii) m(arc QSR)

In the figure, segment PQ is the diameter of the circle with center O. The tangent to the tangent circle drawn from point C on it, intersects the tangents drawn from points P and Q at points A and B respectively, prove that ∠AOB = 90°

**Given:** A circle inscribed in a right angled ΔABC. If ∠ACB = 90° and the radius of the circle is r.

**To prove:** 2r = a + b – c

In a circle with centre P, chord AB is parallel to a tangent and intersects the radius drawn from the point of contact to its midpoint. If AB = `16sqrt(3)`, then find the radius of the circle

In the figure, O is the center of the circle. Line AQ is a tangent. If OP = 3, m(arc PM) = 120°, then find the length of AP.

In the figure, O is the centre of the circle, and ∠AOB = 90°, ∠ABC = 30°. Then find ∠CAB.

In the figure, a circle with center P touches the semicircle at points Q and C having center O. If diameter AB = 10, AC = 6, then find the radius x of the smaller circle.

In the figure, a circle touches all the sides of quadrilateral ABCD from the inside. The center of the circle is O. If AD⊥ DC and BC = 38, QB = 27, DC = 25, then find the radius of the circle.

Circles with centres A, B and C touch each other externally. If AB = 36, BC = 32, CA = 30, then find the radii of each circle.

Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm, and 7 cm. Find the radii of the circles.

The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC.

Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.

Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.

In figure, ∠AOB = 90º and ∠ABC = 30º, then ∠CAO is equal to ______.

If AOB is a diameter of a circle and C is a point on the circle, then AC^{2} + BC^{2} = AB^{2}.

If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC.

In the given figure, O is the centre of the circle. Name all chords of the circle.

In the given figure, O is the centre of the circle. Name a chord, which is not the diameter of the circle.

In the given figure, O is the centre of the circle. Shade sectors OAC and OPB.

From the figure, identify the centre of the circle.

From the figure, identify a diameter.

From the figure, identify two points in the interior.

From the figure, identify a point in the exterior.

Is every diameter of a circle also a chord?

Is every chord of a circle also a diameter?

Draw any circle and mark

- it's centre
- a radius
- a diameter
- a sector
- a segment
- a point in its interior
- a point in its exterior
- an arc

Say true or false:

Two diameters of a circle will necessarily intersect.

A figure is in the form of rectangle PQRS having a semi-circle on side QR as shown in the figure. Determine the area of the plot.

A 7 m broad pathway goes around a circular park with a circumference of 352 m. Find the area of road.

If radius of a circle is 5 cm, then find the length of longest chord of a circle.

AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.

Write answers to the following questions:

- Draw the figure using the given information.
- Find the measures of ∠CAT and ∠ABC with reasons.
- Whether ∠CAT and ∠ABC are congruent? Justify your answer.