A circle with centre has three chords

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

A circle with centre

O

has three chords

AB

CD

and

EF

that subtend central angles of

60^{\circ}

110^{\circ}

and

95^{\circ}

respectively at

O

. (i) Arrange the chords

AB

CD

and

EF

in increasing order of their lengths, clearly stating the reason for every comparison you make. (ii) If the length of

CD

7\,\text{cm}

, explain why the length of

AB

must be less than

7\,\text{cm}

and the length of

EF

must be greater than the length of

AB

but less than

7\,\text{cm}

. Give complete justification for all your statements.