Converse of Theorem 5

Q. In the given figure arc AB and arc CD of a circle having centre at O are equal to 5cm.If $\angle AOB={40}^{\circ }$, then the $\angle COD$ is equal to__.

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

Q. In the given figure arc AB and arc CD of a circle having centre at O are equal to 5cm.If $\angle AOB={30}^{\circ }$, then the $\angle COD$ is equal to__.

1. ${75}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. In the given figure, $PQ$ and $RS$ intersect each other at $O$. If $\angle ROT={75}^o$, find the value of $c$.

1. ${38}^o$
2. ${18}^o$
3. ${46}^o$
4. ${48}^o$

Q.

In the given figure, $\widehat{AB}=\widehat{CD},\angle AOB={55}^{\circ }$ and $\angle BOC={70}^{\circ }$.

Find the value of $\angle COD$

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

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

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

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

Q.

Question 9
Two chords AB and AC of a circle subtends angles equal to ${90}^{\circ }and{150}^{\circ }$ respectively at the centre. Find $\angle BAC$, if AB and AC lie on the opposite sides of the centre.

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

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

Q. If O is the centre of the circle and ∠ ABC=30° then find ∠AOC.

1. ${45}^0$
2. ${30}^0$
3. ${60}^0$
4. ${90}^0$

Q. What is the angle subtended by the major arc of a circle?

1. >180 degrees
2. <180 degrees
3. 180 degrees
4. >360 degrees