The Chords Corresponding to Congruent Arcs Are Congruent

Q.

Chords of a circle, equidistant from the centre are

1. Not equal

2. Perpendicular

3. Parallel

4. Equal

Q. In a circle if two chords are congruent then their corresponding ___________ are congruent.

1. minor arcs
2. major arcs
3. (a) and (b) above.
4. None of the above

Q.

Find the value of x in the diagram below.

Q. Two chords AB and CD of a circle intersect at a point P inside the circle such that AB=12cm, AP=2.4cm, PD=7.2cm, find CD

Q. In the given figure, if angle AOB is 60 degrees and AB = CD then angle DOC = ____.

1. 40 degrees
2. 70 degrees
3. 60 degrees
4. 30 degrees

Q. If chords AB and PQ are equal, angle AOB = 55 degrees, and angle POQ = x, then x = ___.

1. 35 degrees
2. 55 degrees
3. 45 degrees
4. 90 degrees

Q. In the given figure, if $XY=6cm$ and $\angle XOY=\angle MON={85}^{\circ }$, then the length of the chord MN is ___cm.

1. 6

Q.

Two equal chords AB and CD of a circle are such that the length of perpendicular OE on CD = 5 cm. If OF is the perpendicular on AB, then OF =

1. 5 cm

2. 10 cm

3. 15 cm

4. 2.5 cm

Q.

XY and MN are two parallel chords of a circle whose diameter is XM. Then,

1. XY = ¼ MN

2. XY = MN

3. XY = ½ MN

4. XY = 2MN

Q. In the Given Figure, $\angle BAC={90}^{\circ },\angle BAD=\angle CADand\angle DAE=\angle CAE,thenfindthemeasureof\angle BAE$

Q. In a circle, chord MN ≅ chord RT. Chord RT is at a distance of 6 cm from the centre. Find the distance of chord MN from the centre.

Q.

In the adjoining figure, the measure of angle a is 50^o, what is the measure of angle d?

1. 128^o

2. 150^o

3. 108^o

4. 120^o

Q.

In the figure, angle ABC = 65^o and angle ACB = 58^o, the measure of angle BDC is

1. 57^o

2. 45^o

3. 68^o

4. 90^o

Q.

Ram says that two chords are at equal distance from centre but the chords are not equal to each other. Is the statement true or false?

1. True

2. False

Q.

In the figure given below, find$\angle 1,\angle 2,\angle 3,\angle 4and\angle 5$

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. What is the length of the chord MN? [3 Marks]

Q. If arc(AC) and arc(DE) are congruent and AC = 4 cm, then DE = _____.

Q. Two arcs AB and CD subtends equal angle at the centre. if the measure of chord AB is 5 cm then the measure of chord CD is ____.

1. 5 cm
2. 5 cm
3. 8 cm
4. 10 cm

Q. In the Given Figure, $\angle BAC={90}^{\circ },\angle BAD=\angle CADand\angle DAE=\angle CAE,then\angle BAE$
is equal to

Q. In the given figure, what is the value of $x$?

1. 5 cm
2. 6 cm
3. 4 cm
4. 10 cm

Q. In a circle with centre O, the chord PQ ≅ chord AB and m∠AOB = 70°. Find the measure of ∠POQ.

Q.

In the given figure, $O$ is the centre of the circle. $A$ is any point on minor arc $BC$. Find the value of $\angle BAC-\angle OBC$.

1. $90°$

2. $120°$

3. $60°$

4. $45°$

Q. In the Given Figure, $\angle BAC={90}^{\circ },\angle BAD=\angle CADand\angle DAE=\angle CAE,thenfindthemeasureof\angle BAE$

Q. What is the angle between i cap , j cap and k cap.

Q. In the given figure if arc WX = arc YZ, then pair the following with their equivalents.

1. Chord WX
2. $\angle YMZ$
3. WM
4. Chord YZ
5. $\angle WMX$
6. MY

Q. Corresponding arcs of congruent chords of a circle (or congruent circles) need not be congruent.

1. True
2. False

Q. The chords corresponding to congruent arcs of a circle ( or congruent circles) are congruent.

1. True
2. False

Q. Two arcs AB and CD are congruent. if the angle made by arc AB at the centre is 50 degrees then the angle made by arc CD is ______.

1. 60 degrees
2. 70 degrees
3. 40 degrees
4. 50 degrees

Q.

In the given figure, chords $AB=CD,\angle COD={60}^{\circ }$ and $\angle AOD={170}^{\circ }$.

Find the value of $\angle BOC$.

1. ${60}^{\circ }$

2. ${70}^{\circ }$

3. ${75}^{\circ }$

4. ${80}^{\circ }$

Q. In a circle with centre P, chord AB ≅ chord CD and m∠APB = 40°. Find the measure of ∠CPD.