Converse of Theorem 1

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.

Congruent circles that have congruent central angles have

1. congruent chords

2. congruent arcs

3. all of the above

4. none of the above

Q.

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

1. True

2. False

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

Q.

If the two chords in a circle are equal, then the angle it subtends at the centre are equal

1. True

2. False

Q.

In the figure, $XY=6cm,\angle XOY=\angle MON={85}^{\circ }$. The length of the chord $MN$ is

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

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. 4
2. 8
3. 5
4. 6

Q. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection

Q. ABCD is a quadrilateral with right angles at A and C. Points E and F are on the diagonal AC such that DE and BF are both perpendicular to AC. If AE $=3$ cm, DE $=5$ cm and CE $=7$ cm then the length of BF is ______ cm.