Angle Subtended by the Chord at the Centre

Q. In the adjoining figure, O is the centre of the circle whose radius is MN. Measures of some central angles are given. If the measure of the Arc AB is 'a' units and that of Arc CD is 'b' units, then which of the following options is correct.

1. a = b
2. a > b
3. a < b
4. None of the above

Q.

In the given figure, ABCD is a cyclic quadrilateral in which BC = CD and $\angle CBD={35}^{\circ }$. Find $\angle BAD$.

1. 80°
2. 65°
3. 70°
4. 60°

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 the given figure, AB is the diameter of the circle. Find the value of $x$.

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

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${30}^{\circ }$

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

1. supplementary
2. equal
3. complementary

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.

If the angles subtended by two chords of a circle at the centre are equal, then the lengths of the chords are unequal.

1. True

2. False

Q.

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

1. 55${}^{\circ }$

2. 25${}^{\circ }$
3. 35${}^{\circ }$
4. 45${}^{\circ }$

Q.

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

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

2. 55${}^{\circ }$

3. 25${}^{\circ }$
4. 35${}^{\circ }$

Q.

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

1. 8
2. 6
3. 4
4. 5