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CAT 2020 Slot 1 · Quant · Triangles · medium

In triangle ABC, AB = 13, BC = 14 and CA = 15. What is the radius of the circle passing through A, B and C?

Single correct option

In triangle ABC, AB = 13, BC = 14 and CA = 15. What is the radius of the circle passing through A, B and C?
  1. A. 8
  2. B. 8.125
  3. C. 8.5
  4. D. 7.5
Show answer and solution

Answer: (B) 8.125

Area by Heron's formula: s = (13 + 14 + 15)/2 = 21; Area = √(21 × 8 × 7 × 6) = √7056 = 84.

Circumradius R = abc/(4 × Area) = (13 × 14 × 15)/(4 × 84) = 2730/336 = 8.125.

(For comparison, the inradius r = Area/s = 84/21 = 4.)
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Original question written in the CAT 2020 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake