UPSC CAPF AC 2025 Paper 1 · Question 63
Question 63 of the UPSC CAPF (AC) 2025 Paper I (3 August 2025). Try it first, then open the answer and explanation.
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
- 1 : π
- √π : 1
- π : 1
- √π : 2
18 cm, 24 cm और 30 cm भुजाओं वाला एक त्रिभुज एक वृत्त के अंतर्गत है। वृत्त के क्षेत्रफल का त्रिभुज के क्षेत्रफल से अनुपात लगभग कितना है?
- 1 : π
- √π : 1
- π : 1
- √π : 2
Show answer
Answer: (3) π : 1
उत्तर: (3) π : 1
18² + 24² = 324 + 576 = 900 = 30², so the triangle is right-angled and its hypotenuse is a diameter: r = 15 cm. Circle area = 225π cm² and triangle area = 1/2 × 18 × 24 = 216 cm², so the ratio is 225π : 216 ≈ 1.04π : 1, i.e. about π : 1.