In a circle with centre

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

Problem

O

, chords

AB

and

CD

are equal. The angles subtended at the centre by these chords are

\angle AOB = (4y - 10)^{\circ}

and

\angle COD = (3y + 20)^{\circ}

. (i) Prove that arcs

AB

and

CD

are equal. (ii) Using the result of part (i), form an equation in

y

and hence find the value of

y

. (iii) Determine the common measure of arcs

AB

and

CD

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