In a circle, points and are taken in that order on the circumference. Chord is drawn,…

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

Problem

In a circle, points A,B,C,A, B, C, and DD are taken in that order on the circumference. Chord ACAC is drawn, and points BB and DD lie in the same segment with respect to chord ACAC. (i) If ∠ABC=3x∘\angle ABC = 3x^{\circ} and ∠ADC=(x+60)∘\angle ADC = (x + 60)^{\circ}, find xx. (ii) Given that ∠BAD=52∘\angle BAD = 52^{\circ}, calculate ∠BCD\angle BCD.

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