In a circle with centre

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

Problem

O

, two chords

AB

and

CD

are equal in length. The chord

AB

subtends an angle of

(3x+15)^{\circ}

at the centre, while chord

CD

subtends an angle of

(5x-25)^{\circ}

at the centre. (i) Find the value of

x

. (ii) Determine the common measure of the two central angles. (iii) A third chord

EF

subtends an angle of

100^{\circ}

at the centre. Arrange the three chords

AB,\,CD

and

EF

in increasing order of length, giving reasons for your answer.