| 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.