Multiple choice

$ABC$ is a triangle in which $\angle\ B=90^{o},\ BC=48\ cm$ and $AB=14\ cm$. A circle is inscribed in the triangle, whose centre is $O$. Find radius $r$ of in-circle.

  1. $4\ cm$
  2. $6\ cm$
  3. $7\ cm$
  4. $9\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle with legs a and b and hypotenuse c, the inradius r = (a + b - c) / 2. Here, a = 14, b = 48, and c = sqrt(14^2 + 48^2) = sqrt(196 + 2304) = sqrt(2500) = 50. Thus, r = (14 + 48 - 50) / 2 = 12 / 2 = 6.

AI explanation

Using the Pythagorean theorem for right triangle ABC, the hypotenuse AC is sqrt(14^2 + 48^2) = sqrt(196 + 2304) = 50 cm. The formula for the radius of an incircle in a right triangle is r = (sum of legs - hypotenuse) / 2. Therefore, r = (14 + 48 - 50) / 2 = 6 cm, resulting in 6 cm.

Keep practicing — related questions