###### Advertisements

###### Advertisements

If O is the center of the circle in the figure alongside, then complete the table from the given information.

The type of arc

Type of circular arc |
Name of circular arc |
Measure of circular arc |

Minor arc | ||

Major arc |

###### Advertisements

#### Solution

Type of arc |
Name of the arc |
Measure of the arc |

Minor arc | arc AXB |
100° |

Major arc | arc AYB |
260° |

#### APPEARS IN

#### RELATED QUESTIONS

In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. Write the measure of ∠OAB.

In Fig. 2, AB is the diameter of a circle with centre O and AT is a tangent. If ∠AOQ = 58°, find ∠ATQ.

n Fig. 2, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then ∠QOR equals:

(A) 67°

(B) 134°

(C) 44°

(D) 46°

In the given figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects PQ at A and RS at B. Prove that ∠AOB = 90º

Fill in the blanks:

The centre of a circle lies in ____________ of the circle.

Write True or False. Give reason for your answer.

A circle has only finite number of equal chords.

A point P is 26 cm away from O of circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius 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.

From a point P, two tangents PA and PB are drawn to a circle with center O. If OP =

diameter of the circle shows that ΔAPB is equilateral.

In fig.. O is the center of the circle and BCD is tangent to it at C. Prove that ∠BAC +

∠ACD = 90°

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 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.

In the following figure, AB is the diameter of a circle with centre O and CD is the chord with length equal to radius OA.

Is AC produced and BD produced meet at point P; show that ∠APB = 60°

Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 50° then what is the measure of ∠OAB.

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC ?

If *ABCD* is a cyclic quadrilateral in which *AD* || *BC* (In the given figure). Prove that ∠*B* = ∠*C*.

In a cyclic quadrilateral *ABCD*, if *m *∠*A* = 3 (*m* ∠*C*). Find *m* ∠*A*.

In the given figure, *O* is the centre of the circle and ∠*DAB* = 50° . Calculate the values of *x*and *y*.

*ABC* is a triangle with *B* as right angle, *AC *= 5 cm and *AB* = 4 cm. A circle is drawn with* A*as centre and *AC *as radius. The length of the chord of this circle passing through *C* and *B* is

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

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.

In the given figure, AB is a diameter of a circle with centre O and AT is a tangent. If \[\angle\] AOQ = 58º, find \[\angle\] ATQ.

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 ______.

AB and CD are two equal chords of a drde intersecting at Pas shown in fig. P is joined to O , the centre of the cirde. Prove that OP bisects ∠ CPB.

Find the area of a circle of radius 7 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)

**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 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

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

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

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

R is the _______ of the circle.

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

Diameter of a circle is ______.

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

Diameter = 2 x ________

Draw circle with diameter: 8.4 cm

In above case, measure the length of the radius of the circle drawn.

Draw a circle of radius 6 cm. In the circle, draw a chord AB = 6 cm.

(i) If O is the center of the circle, join OA and OB.

(ii) Assign a special name to ∆AOB

(iii) Write the measure of angle AOB.

Mark two points A and B ,4cm a part, Draw a circle passing through B and with A as a center

Draw a line AB = 8.4 cm. Now draw a circle with AB as diameter. Mark a point C on the circumference of the circle. Measure angle ACB.

Construct a triangle ABC with AB = 5 cm, ∠B = 60° and BC = 6. 4 cm. Draw the incircle of the triangle ABC.

**State, if the following statement is true or false:**

If the end points A and B of the line segment lie on the circumference of a circle, AB is a diameter.

**State, if the following statement is true or false:**

The diameters of a circle always pass through the same point in the circle.

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 _______________

The ______________ is the longest chord of a circle

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

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 the adjoining figure, seg DE is the chord of the circle with center C. seg CF⊥ seg DE and DE = 16 cm, then find the length of DF?

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.

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ______

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.

A point A is 26 cm away from the centre of a circle and the length of the tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

In figure, if ∠ABC = 20º, then ∠AOC is equal to ______.

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

O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

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 all radii 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 the smaller segment of the circle formed by CP.

From the figure, identify three radii.

From the figure, identify a sector.

From the figure, identify a segment.

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.

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

**Assertion (A):** If the circumference of a circle is 176 cm, then its radius is 28 cm.

**Reason (R):** Circumference = 2π × radius 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.