Points and lie on a circle

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

Problem

Points A,B,CA, B, C and DD lie on a circle. The chord ABAB subtends ∠ACB=40∘\angle ACB = 40^{\circ} at point CC and ∠ADB=4x−20∘\angle ADB = 4x - 20^{\circ} at point DD on the same side of ABAB. The chord ACAC subtends ∠ABC=3x+5∘\angle ABC = 3x + 5^{\circ} at point BB. (i) Find the value of xx. (ii) Calculate ∠ADB\angle ADB and ∠ABC\angle ABC. (iii) Hence, determine the measure of ∠ADC\angle ADC.

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