###### Advertisements

###### Advertisements

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

________ is a radius of the circle.

###### Advertisements

#### Solution

**RS** is a radius of the circle.

#### APPEARS IN

#### RELATED QUESTIONS

From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.

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 blanks:

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

If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ= 24cm and OQ = 25 cm. Find the radius of circle

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at center.

In Fig below, PQ is tangent at point R of the circle with center O. If ∠TRQ = 30°. Find

∠PRS.

Two tangent segments PA and PB are drawn to a circle with center O such that ∠APB =120°. Prove that OP = 2AP

In fig. a circle touches all the four sides of quadrilateral ABCD with AB = 6cm, BC = 7cm, CD = 4cm. Find AD.

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

∠ACD = 90°

In the given figure, *AB* is a chord of length 16 cm of a circle of radius 10 cm. The tangents at *A* and* B* intersect at a point *P*. Find the length of *PA*.

In figure PA and PB are tangents from an external point P to the circle with centre O. LN touches the circle at M. Prove that PL + LM = PN + MN

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 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°

In the given figure, PA and PB are the tangent segemtns to a circle with centre O. Show that he points A, O, B and P are concyclic.

In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that point of contact P bisects the base BC.

In the given figure, Δ*ABC* is an equilateral triangle. Find *m*∠*BEC*.

A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is

One chord of a circle is known to be 10 cm. The radius of this circle must be

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

In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

If \[d_1 , d_2 ( d_2 > d_1 )\] be the diameters of two concentric circle s and *c* be the length of a chord of a circle which is tangent to the other circle , prove that\[{d_2}^2 = c^2 + {d_1}^2\].

In the given figure, *BC* is a tangent to the circle with centre *O*. *OE* bisects *AP.* Prove that ΔAEO ∼ Δ ABC.

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 13 cm and the distance from the centre is 12 cm

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

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.

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.

If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

Find the area of a circle of radius 7 cm.

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.

In the given figure, seg MN is a chord of a circle with centre O. MN = 25, L is a point on chord MN such that ML = 9 and d(O,L) = 5. Find the radius of the circle.

**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 above figure, seg AB is a diameter of a circle with centre P. C is any point on the circle. seg CE ⊥ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of the following steps:

a. Draw ray CE. It intersects the circle at D.

b. Show that CE = ED.

c. Write the result using the theorem of the intersection of chords inside a circle. d. Using CE = ED, complete the proof.

Two concentric circles with center O have A, B, C, D as the points of intersection with the lines L shown in the figure. If AD = 12 cm and BC s = 8 cm, find the lengths of AB, CD, AC and BD.

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.

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:**

______ is a chord of the circle.

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

AB is a ______ of the circle.

Draw circle with diameter: 6 cm

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

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 âˆ†AOB

(iii) Write the measure of angle AOB.

The center of a circle is at point O and its radius is 8 cm. State the position of a point P (point P may lie inside the circle, on the circumference of the circle, or outside the circle), when:

(a) OP = 10.6 cm

(b) OP = 6.8 cm

(c) OP = 8 cm

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.

**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:**

Every diameter bisects a circle and each part of the circle so obtained is a semi-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 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 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, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).

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 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 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.

If the angle between two radii of a circle is 130°, then the angle between the tangents at the ends of the radii is ______

If the angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre ‘O’ is 90°, then OP = ______

If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents at A and B is ______

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.

If a number of circles pass through the endpoints P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.

If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure. Prove that ∠BAT = ∠ACB

In figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to ______.

If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C.

If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.

The circumcentre of the triangle ABC is O. Prove that ∠OBC + ∠BAC = 90º.

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

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

From the figure, identify the centre of the circle.

From the figure, identify three radii.

From the figure, identify a chord.

From the figure, identify a sector.

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.