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Question

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle. If ADC=130, find BAC.


A

(1202)

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B

(1203)

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C

60

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D

40

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Solution

The correct options are
B

(1203)


D

40


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


D+B=180 [Sum of opposite angles of a cyclic quadilateral is 180]

130+B=180

B=180130=50

ACB=90 [Angle subtended by diameter on the circle is 90]

In ΔABC,

BAC+ACB+CBA=180 [Sum of angles of a triangle is 180]
BAC+50+90=180

BAC=1809050=40


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