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Question

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If BAC=30, then find CDB.


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Solution

ACB=90 (angles in the semicircle)
BCD=30 ( angles in the alternate segment are equal) [1 mark]
ACD=ACB+BCD
=90+30=120
CDB=180(30+120) .....(sum of angles in a triangle)
=180150=30 [1 mark]

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