Area of Triangle in Semi-circle

CAT 1996 Slot 1 · Quantitative Ability · Easy · QA

This is an easy Quantitative Ability question from the CAT 1996 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

A circle has diameter $AB = 13\text{ cm}$ (radius $6.5\text{ cm}$). If chord $CA = 5\text{ cm}$, find the area of $\triangle ABC$.

1. A.

   60 sq. cm

2. B.

   30 sq. cm

3. C.

   40 sq. cm

4. D.

   52 sq. cm

Answer & explanation hiddenTry it firstShow answer

Answer

B

Explanation

Angle in a semicircle $\angle ACB = 90^\circ$. $BC = \sqrt{13^2 - 5^2} = 12\text{ cm}$. $\text{Area} = \frac{1}{2} \times 5 \times 12 = 30\text{ sq. cm}$.