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NDA 2023 Maths · Mathematics · Properties of Triangles · medium

The radius of its incircle is

Single correct option

The sides of a triangle are 1313, 1414 and 1515. The radius of its incircle is
  1. A. 88
  2. B. 44
  3. C. 658\dfrac{65}8
  4. D. 66
Show answer and solution

Answer: (B) 44

The semi-perimeter is s=21s=21 and Heron's formula gives area Δ=21⋅8⋅7⋅6=84\Delta=\sqrt{21\cdot8\cdot7\cdot6}=84. The inradius is r=Δ/s=84/21=4r=\Delta/s=84/21=4. Option 658\tfrac{65}8 is the circumradius abc/4Δabc/4\Delta, which is a different quantity.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake