2025 · Q63
A triangle of sides 18 cm, 24 cm and 30 cm is inscribed in a circle. The ratio of the area of the circle to that of the triangle is approximately
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- A1 : π
- B√π : 1
- Cπ : 1
- D√π : 2
Explanation
Since 18^2+24^2 = 324+576 = 900 = 30^2, the triangle is right-angled with area (18x24)/2 = 216 sq cm. For a right triangle inscribed in a circle, the hypotenuse is the diameter, so the circumradius is 15 cm and the circle's area is pi x 15^2 = 225 pi. The ratio circle:triangle = 225 pi : 216, approximately pi : 1.