Converse of Chord Theorem 1

Q.

In a circle of radius 5 cm, $AB$ and $AC$ are two chords such that $AB=AC=6cm.$ Find the length of the chord $BC$.

1. 5.6 cm

2. 10.6 cm

3. 9.6 cm

4. 11.6 cm

Q.

A chord AB of a circle whose centre is O, is bisected at E by a diameter CD. OC= OD = 15cm and OE = 9 cm. Find the length of AB.

1. 12 cm
2. 18 cm
3. 24 cm
4. 30 cm

Q.

A chord $AB$ of a circle whose center is $O,$ is bisected at $E$ by a diameter $CD.$ $OC=OD=15cm$ and $OE=9cm.$ Find the length of $BC.$

1. $12\sqrt{5}cm$

2. $10\sqrt{3}cm$

3. $6\sqrt{10}cm$

4. $12cm$

Q. In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={60}^{\circ }$, then $\angle CAO$ is equal to__.

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

Q. A circle has a radius of 5 cm and a chord AB of 8 cm. How far is the midpoint of the chord from the centre of the circle?

1. 5 cm
2. 4 cm
3. 3 cm
4. 2.5 cm

Q.

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

1. 4 cm

2. 5 cm

3. 3 cm

4. 3.5 cm

Q. In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={50}^{\circ }$, then $\angle CAO$ is equal to__.

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

Q.

A chord AB of a circle whose centre is O, is bisected at E by a diameter CD. OC= OD = 15 cm and OE = 9 cm. Find the length of AD.

1. $5\sqrt{5}cm$

2. $6\sqrt{5}cm$

3. $5cm$

4. $6cm$

Q.

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is $2\sqrt{5}$ cm, then find the distance of the chords from the centre and the length AC.

1. 2.35 cm, 2 cm

2. 3 cm, 2 cm

3. 2.16 cm, 2.346 cm

4. 2 cm, 2.346 cm

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. In a circle of radius $5cm,AB$ and $CD$ are two parallel chords of lengths $8cm$ and $6cm$ respectively.
Calculate the distance between the chords if they are on opposite sides of the centre.