The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of ΔABC.
Explanation:
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 =12 × AC × CB = 12 × 5 × 12 = 30 sq.cm.
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