| 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.