Question
In a circle AB is diameter and points C and D are on
the circumference such that ∠CAD = 40° and ∠CBA = 60°. What is the value of ∠ACD?Solution
According to figure above, ∠CAD and ∠CBD subtend the same arc DC on the circumference. ⇒∠CAD = ∠CBD = 40° Also, ∠DBA = ∠CBA - ∠CBD = 60 - 40 = 20°. Now ∠DBA and ∠ACD subtend the same arc DA on the circumference of the circle. ⇒∠ACD = ∠DBA = 20°.
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