Multiple choice

$\bigtriangleup$ABC is a right angled triangle with $\angle A = 90^{\circ}$.A circle is inscribed in it. The lengths of the sides containing the right angle are 6 cm and 8 cm.Find the radius of the circle.

  1. $3 cm$
  2. $3.5 cm$
  3. $2.5 cm$
  4. $2 cm$
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D Correct answer
Explanation

For a right triangle with legs a and b and hypotenuse c, the inradius r = (a + b - c) / 2. Here, legs are 6 and 8, so hypotenuse c = 10. r = (6 + 8 - 10) / 2 = 4 / 2 = 2.

AI explanation

First, find the hypotenuse of the right triangle using the Pythagorean theorem, which is the square root of (6 squared + 8 squared) = 10 cm. The formula for the inradius of a right triangle is r = (sum of the perpendicular legs - hypotenuse) / 2. Substituting the values gives r = (6 + 8 - 10) / 2. This simplifies to 4 / 2, resulting in a radius of 2 cm.

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