# Chord Theorem 2

## Trending Questions

**Q.**Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

**Q.**

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD.

**Q.**8.Chord AB of the circle xÂ²+yÂ², =100 passes through the point (7, 1) and substends an angle of 60 at the circumference of the circle.If m1 and m2 are the slopes of 2 such chords then the value of m1.m2 is

**Q.**In the given figure, AB and CD are two equal chords of the circle with centre O. OP and OQ are perpendiculars of the chord AB and CD respectively. If ∠POQ=80∘, then what is the value of ∠APQ?

- 50∘
- 40∘
- 30∘
- 60∘

**Q.**Question 8

The area of the square that can be inscribed in a circle of radius 8 cm is

(A) 256 cm2

(B) 128 cm2

(C) 64√2 cm2

(D) 64 cm2

**Q.**The perpendicular drawn from the centre of the circle to a chord divides the chord in the ratio

- 2:1
- 1:2
- 1:1

**Q.**

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E . If CD =16 cm and EB = 4 cm, then find the radius of the circle.

6 cm

8 cm

10 cm

11 cm

**Q.**

Distance between equal chords, AB and CD of a circle with centre, O and radius, 5 cm is 8 cm. Find the length of the the chords.

8 cm

6 cm

10 cm

12 cm

**Q.**

In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 24 cm and OD = 5 cm, then find the circumradius.

10 cm

11 cm

12 cm

13 cm

**Q.**

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP > PB. Then, AP is–

24 cm

8 cm

6 cm

12 cm

**Q.**

$PQ\text{and}RQ$ are chords of a circle equidistant from the centre. Prove that the diameter passing through $Q$ bisects $\xe2\u02c6PQR\text{and}\xe2\u02c6PSR$.

**Q.**

O is the centre of the circle of radius 5 cm, OP is perpendicular to AB, OQ is perpendicular to CD, AB||CD, AB=6 cm and CD=8 cm. Determine PQ.

2 cm

1 cm

3 cm

4 cm

**Q.**

In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:

4 cm, 4 cm

4 cm, 8 cm

8 cm, 4 cm

8 cm, 8 cm

**Q.**

In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle.

√119 cm

√113 cm

√117 cm

√114 cm

**Q.**

The figure is a circle with centre O and diameter 10 cm. PQ = 1 cm. Then the length of RS is

3 cm

6 cm

4 cm

8 cm

**Q.**The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm, then find the length of the chord MN.

**Q.**

Draw a circle on a tracing paper and draw two equal chords and drop a perpendicular from center to the chord. Fold the paper such that the two chords coincide. You will find that the two perpendiculars also coincide.

True

False

**Q.**

Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below.

Then which of the following is/are true?

AP + DP = CP + BP

BP = DP, but AP ≠ CP

AP = CP and BP = DP

AP = CP, but BP ≠ DP

**Q.**

In the figure, P and Q are the points of intersection of two circles with centres O and O′. If straight lines, APB and CQD are parallel to OO′, then what is the ratio of OO′ and AB?

1:3

1:2

1:4

3:4

**Q.**

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the distance between AB and CD.

8 cm

7 cm

11 cm

10 cm

**Q.**

In the adjoining figure, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, then which of the following are true?

AC=2 OD

ACDO=BCBO

ACBO=BCDO

OD∥AC

**Q.**

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm & 34 cm, the distance between their centers is ____ cm.

30

28

24

32

**Q.**

AB & CD are two equal chords of a circle with centre O which intersect each other at the right angle at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a _______.

square

kite

rhombus

rectangle

**Q.**

Four points A, B, C, D are given on a circle. Line segment AB and CD are parallel. Find the area of the figure formed by joining these points (in cm2).

98

49

7

28

**Q.**

In the given figure, a circle with centre O has diameter 16 cm. If PQ = 2 cm, then the measure of RS is

2√7 cm

2√28 cm

√28 cm

4√7 cm

**Q.**A chord of length 30 cm is drawn at a distance of 8 cm from the centre of a circle. Find out the radius of the circle.

**Q.**

S1: AM = AP2, BN= BP2

S2: OO' = AM + BN

Which of the above statements are true?

Only S1 is true.

Only S2 is true.

S1 is true & S2 is false.

Both statements are true.

**Q.**

In the diagram, select the major arc and the minor arc of the circle, with respect to the chord AB.

AYBA, AXBA

XAYX, XBYX

AXBA, AYBA

XBYX, XAYX

**Q.**

An equilateral triangle ABC is inscribed in a circle with centre O. Then, ∠BOC is equal to:

30°

60°

90°

120°

**Q.**

In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

4 cm

5 cm

8 cm

10 cm