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Question

In the given figure, ABC is inscribed in a circle. The bisector of BAC meets BC at D and the circle at E. If EC is joined and ECD =30o, find BAC.

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A
30o
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B
40o
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C
50o
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D
60o
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Solution

The correct option is D 60o
Given, AD is perpendicular bisector of BC
and ECD=30o
In DCE
DEC=180(DCE+CDE)DEC=180(30+90)DEC=60o
Also, ABC=AEC=60 (half angle property)
In ABD
ADB=90o,ABD=60o
Hence,
BAD=180(90+60)=30o
BAC=2BAD=60o (angular bisector)

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