In a circle with centre O, AB is the diameter and CD is a chord such t

| In a circle with centre O, AB is the diameter and CD is a chord such that ABCD is a trapezium. If BAC = 24°, then CAD is equal to:

A. 36

B. 42

C. 48

D. 24

Right Answer is: B

SOLUTION

In the diagram shown below, triangle ABC is right angled triangle (Angle subtended by a diameter/semicircle on any point of circle is 90 degrees). So ACB= 90, BAC = 24°

Then, ABC = 180 – (90+24) = 66
As given that ABCD is a trapezium so, CD must be parallel to AB.
Hence,
DCA = BAC = 24
Using cyclic quadrilateral theorem, sum of opposite angles of cyclic quadrilateral is 180.
So,
ADC + ABC = 180

ADC + 66 = 180

ADC = 114

In triangle ADC, sum of angles CAD + ACD + ADC = 180

CAD + 24 + 114 = 180

CAD = 180-138= 42
Hence, option B is the correct answer.

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