A circle has a fixed chord

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

Problem

A circle has a fixed chord ABAB. Points CC and DD lie on the circumference on the same side of ABAB. (i) State the relation between the angles subtended by a chord at any two points on the same segment of a circle. (ii) Using the result of part (i), show that ∠ACB=∠ADB\angle ACB=\angle ADB. (iii) If ∠ACB=58∘\angle ACB=58^\circ, calculate the measure of ∠ADB\angle ADB. The construction and reasoning steps must be clearly explained.

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