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Question

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ADC=130, then find BAC.

A
50
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B
25
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C
60
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D
40
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Solution

The correct option is D 40

Given: ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle and ADC=130.

To find BAC:


Since opposite angles of a cyclic quadilateral are supplementary, we have
D+B=180.

i.e., 130+B=180

B=180130=50

Since an angle in a semicircle is a right angle, we have
ACB=90.

In ΔABC,

BAC+50+90=180. (Angle sum property)

BAC=1809050=40


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