Exams › SSC CGL (Prelims) › General

A right triangle has legs of length p and q and hypotenuse r. What is the inradius (radius of the inscribed circle)?

1. (p + q - r) / 2
2. (p + q + r) / 2
3. (p^2 + q^2) / r
4. pqr / (p + q + r)

Correct answer: (p + q - r) / 2

Solution

For a right-angled triangle, the inradius equals (leg1 + leg2 - hypotenuse)/2. Substituting the legs p, q and hypotenuse r gives r_in = (p + q - r)/2.

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