Equal Chords of a Circle

Q. Angles subtended by equal chords at the centre of the circle are .

1. supplementary
2. equal
3. complementary

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ = ___.

1. ${50}^{\circ }$

2. ${40}^{\circ }$

3. ${65}^{\circ }$

4. ${70}^{\circ }$

Q.

ABC and ADC are two right triangles with common hypotenuse AC. Prove that $\angle \mathrm{CAD}=\angle \mathrm{CBD}$.

Q.

In the following figure, if chords AB and CD are equal to 6 cm, then the distances of the chords from the centre of the circle of radius 5 cm are ___ and ___ respectively.

1. 4 cm, 4 cm

2. 4 cm, 8 cm

3. 8 cm, 8 cm

4. 8 cm, 4 cm

Q.

Consider the above figure where $O$ is the center of the circle, $AB=CD$ and $\angle AOB={30}^{\circ }.$ Then, $\angle AED$ = ___ and $\angle COD$ = ___.

1. ${60}^{\circ },{30}^{\circ }$
2. ${30}^{\circ },{90}^{\circ }$
3. ${90}^{\circ },{30}^{\circ }$
4. ${80}^{\circ },{50}^{\circ }$

Q.

In the given figure, ON = OM. If AB = 5 cm, then CD is equal to:

1. 4 cm

2. 7 cm

3. 5 cm

4. 6 cm

Q. Question 4
Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that $\angle ABC$ is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

Q. In the given figure, O is the centre of the circle. If $\angle AOB={100}^{\circ }$ and $\angle AOC={90}^{\circ }$, then find $\angle BAC$.

1. ${85}^{\circ }$
2. ${90}^{\circ }$
3. ${80}^{\circ }$
4. ${75}^{\circ }$

Q. In the given figure, arc AB and arc BC are equal in length. If $\angle AOB={48}^o$, find
(i) $\angle BOC$
(ii) $\angle OBC$
(iii) $\angle AOC$
(iv) $\angle OAC$

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ = ___.

1. ${50}^{\circ }$

2. ${65}^{\circ }$

3. ${40}^{\circ }$

4. ${70}^{\circ }$

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ = ___.

1. ${40}^{\circ }$

2. ${50}^{\circ }$

3. ${70}^{\circ }$

4. ${65}^{\circ }$

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 $\angle POQ={80}^{\circ }$ then what is the value of $\angle APQ$?

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 $\angle POQ={80}^{\circ },$ then what is the value of $\angle APQ$ in degrees?

1. 40

Q.

In the given figure, the radius of the circle is 4 cm and ∠POS = 90° . Find the length of QR.

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 $\angle POQ={80}^{\circ },$ then what is the value of $\angle APQ$ in degrees?

1. 40

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ (in degrees) = ___.

1. 65

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 $\angle POQ={80}^{\circ },$ then what is the value of $\angle APQ$?

1. ${60}^{\circ }$
2. ${50}^{\circ }$
3. ${30}^{\circ }$
4. ${40}^{\circ }$

Q. In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, $OD\perp PQ$ and $OE\perp RS$ . If $\angle DOE={130}^{\circ }$ then find $\angle PDE$

Q.

If chords AB and PQ are equal, $\angle AOB={55}^{\circ }$, and $\angle POQ=x,$ then $x$ = ___.

1. 35${}^{\circ }$
2. 45${}^{\circ }$

3. 55${}^{\circ }$

4. 25${}^{\circ }$

Q. If PQ = RS and $\angle ORS={48}^{\circ }$ in the given figure, what are the values of $\angle OPQ$ and $\angle SOR$?

1. ${84}^{\circ }$, ${48}^{\circ }$
2. ${48}^{\circ }$, ${84}^{\circ }$
3. ${38}^{\circ }$, ${68}^{\circ }$
4. ${78}^{\circ }$, ${84}^{\circ }$

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ = ___.

1. ${50}^{\circ }$

2. ${65}^{\circ }$

3. ${40}^{\circ }$

4. ${70}^{\circ }$

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

1. 2:1
2. 1:2
3. 1:1

Q. In the figure, O is the centre of the circle. Find the length of CD, if AB=5 cm.

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

Q. Equal chords subtend equal angles at the centre.

1. False
2. True

Q. If chords AB and PQ are equal, $\angle AOB={55}^{\circ }$, and $\angle POQ=x,$ then find the value of $x$.

1. 55${}^{\circ }$
2. 25${}^{\circ }$
3. 50${}^{\circ }$
4. 45${}^{\circ }$

Q. Find the value of $x$ in the given figure if $\angle AOB={70}^{\circ }$ and $AB=CD.$

1. ${70}^{\circ }$
2. ${60}^{\circ }$
3. ${80}^{\circ }$
4. ${40}^{\circ }$

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ = ___.

1. ${50}^{\circ }$

2. ${65}^{\circ }$

3. ${40}^{\circ }$

4. ${70}^{\circ }$

Q.
Using the information given in the figure match the following :

1. y cm
2. $x^{\circ }$
3. 90°- x°2
4. $\frac{y}{2}$ cm

Q.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $\perp$ PQ and OE $\perp$ RS. If $\angle DOE={130}^{\circ },$ then $\angle PDE$ (in degrees) = ___.

1. 65

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 $\angle POQ={80}^{\circ },$ then what is the value of $\angle APQ$?

1. ${60}^{\circ }$
2. ${50}^{\circ }$
3. ${30}^{\circ }$
4. ${40}^{\circ }$