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 = 25°, then CAD is equal to:

A. 45°

B. 40°

C. 25°

D. 65°

Right Answer is: B

SOLUTION

In the diagram shown above, triangle ABC is right angled triangle. So ACB= 90, BAC = 25°

Then, ABC = 180 – (90+25) = 65
As given that ABCD is a trapezium so, CD must be parallel to AB.
Hence,
DCA = BAC = 25
Using cyclic quadrilateral theorem, sum of opposite angles of cyclic quadrilateral is 180.
So,
ADC + ABC = 180

ADC + 65 = 180
ADC = 115
In triangle ADC, sum of angles
CAD + ACD + ADC = 180
CAD + 25 + 115 = 180
CAD = 180-140 = 40
Hence, option B is the correct answer.

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