CAT 1996 — QA Question 11

The radius of the circle is 6.5 cm. Therefore, its diameter = 13 cm and AB = 13 cm. Since the diameter of a circle
subtends 90° at the circumference, ∠ACB = 90°. So ΔACB is a right-angled triangle with AC = 5, AB = 13.

Therefore, CB should be equal to 12 cm (as 5-12-13 form a Pythagorean triplet).

Hence, the area of the triangle $=\frac{1}{2}$ × AC × CB = $\frac{1}{2}$ × 5 × 12 = 30 sq.cm.