Converse of Chord Theorem 2

Q.

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the center makes equal angles with the chords.

Q.

Chords AB and CD of a circle with centre O, intersect at a point E. If OE bisects $\angle$AED, then chord AB = CD.

1. True

2. False

Q.

The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC. [4 Marks]

Q.

Two equal chords, $AB$ and $CD$ are at a distance of 10 cm from each other. Find the distance of chord $AB$ from the centre.

1. $6cm$

2. $5cm$

3. $20cm$

4. $12cm$

Q.

If each of two chords, $AB$ and $CD$, of a circle are at a distance of 4 cm from the centre, then $AB=CD$.

1. True

2. False

Q. In the given figure AB and CD are two chord of a circle having centre at O.Two perpendicular line OE and OF having equal lenghs are drawn as shown.If AB = 12 cm , then the length of FD is equal to__.

1. 6 cm
2. 12 cm
3. 24 cm
4. 18 cm

Q.

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

1. 4 cm

2. 5 cm

3. 6 cm

4. 7 cm

Q. In the given figure AB and CD are two chords of a circle having centre at O.Two perpendicular lines OE and OF are having equal lenghs are drawn as shown.If AB = 10 cm , then the length of CD is equal to

1. 5 cm
2. 7.5 cm
3. 10 cm
4. 15 cm