Multiple choice

In a right triangle $ABC$, right-angled at $B, BC=12 cm$ and $AB = 5 cm$. The radius of the circle inscribed in the triangle (in cm) is

  1. $4$
  2. $3$
  3. $2$
  4. $1$
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C Correct answer
Explanation

For a right triangle with sides a, b and hypotenuse c, the inradius r = (a + b - c) / 2. Here, a=5, b=12, c=sqrt(5^2 + 12^2) = 13. r = (5 + 12 - 13) / 2 = 4 / 2 = 2.

AI explanation

First, find the hypotenuse AC using the Pythagorean theorem: sqrt(5^2 + 12^2) = sqrt(169) = 13 cm. For a right-angled triangle, the radius of the inscribed circle is given by the formula r = (sum of perpendicular sides - hypotenuse) / 2. Substituting the known values gives r = (5 + 12 - 13) / 2 = 4 / 2 = 2 cm.

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