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Question

In the figure, AB is a diameter, BAC=38o. Find ADC.
559572_67caadabe4074b04816107bf2274ddce.png

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Solution

Given that:
BAC=38 and AB is a diameter.
To find:
ADC=?
Solution:
Since, AB is a diameter.
ACB=90
In ACB
BAC+ACB+ABC=180
or, 38+90+ABC=180
or, ABC=52
Now,
Since ABCD is a cyclic quadrilateral.
ADC+ABC=180 (sum of opposite angles of a cyclic quadrilateral is 180.)
or, ADC+52=180
or, ADC=128

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