In a circle with centre

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

Problem

O

, three points

A

B

and

C

lie on the circumference such that

\angle AOB=100^{\circ}

\angle AOC=60^{\circ}

and

\angle BOC=140^{\circ}

. (i) Prove that chord

AB

is longer than chord

AC

. (ii) Prove that chord

BC

is longer than chord

AC

. (iii) Arrange the three chords

AB

BC

and

AC

in descending order of their lengths, supplying clear reasons for each step of your arrangement.