Area of Triangle in Semi-circle

CAT 1996 Slot 1 · QA · Easy · QA

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A circle has diameter AB=13 cmAB = 13\text{ cm} (radius 6.5 cm6.5\text{ cm}). If chord CA=5 cmCA = 5\text{ cm}, find the area of △ABC\triangle ABC.

  1. A.

    60 sq. cm

  2. B.

    30 sq. cm

  3. C.

    40 sq. cm

  4. D.

    52 sq. cm

Answer

B

Explanation

Angle in a semicircle ∠ACB=90∘\angle ACB = 90^\circ. BC=132−52=12 cmBC = \sqrt{13^2 - 5^2} = 12\text{ cm}. Area=12×5×12=30 sq. cm\text{Area} = \frac{1}{2} \times 5 \times 12 = 30\text{ sq. cm}.

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