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NDA 2025 Maths · Mathematics · Properties of Triangles · medium

A triangle: 1. For a triangle with sides 5,12,13, the circumradius is 6.5. 2. In every triangle the circumcentre lies inside the triangle.

Single correct option

Consider the following statements about a triangle:
1. For a triangle with sides 5,12,135,12,13, the circumradius is 6.56.5.
2. In every triangle the circumcentre lies inside the triangle.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

Since 52+122=1325^2+12^2=13^2, the triangle is right-angled and the circumcentre is the midpoint of the hypotenuse, so R=132=6.5R=\frac{13}2=6.5. Statement 2 is false: for an obtuse triangle the circumcentre lies outside, and for a right triangle on the hypotenuse.
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Original question written in the NDA 2025 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