Multiple choice

$ABC$ is a right angle triangle right angled at $A.$ A circle is inscribed in it. The lengths of two sides containing the right angle are $6$ cm and $8$ cm. Find the radius of the circle$: ?$

  1. $3$ cm
  2. $2$ cm
  3. $5$ cm
  4. $4$ cm
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B Correct answer
Explanation

In a right triangle with legs a=6 and b=8, the hypotenuse c = sqrt(6^2+8^2) = 10. The inradius r of a right triangle is (a+b-c)/2 = (6+8-10)/2 = 4/2 = 2 cm.

AI explanation

Calculate the hypotenuse of the triangle using the Pythagorean theorem, which is the square root of (6 squared + 8 squared) = 10 cm. Apply the right triangle inradius formula, which is r = (leg1 + leg2 - hypotenuse) / 2. Inserting the side lengths gives r = (6 + 8 - 10) / 2. This simplifies to 4 / 2, so the radius is 2 cm.

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