Multiple choice

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

  1. 2 cm

  2. 6 cm

  3. 8 cm

  4. 10 cm
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A Correct answer
Explanation

For a right triangle with legs a and b and hypotenuse c, the inradius r is given by (a + b - c) / 2. Here, a=6, b=8, so c = sqrt(6^2 + 8^2) = 10. Thus, r = (6 + 8 - 10) / 2 = 4 / 2 = 2 cm.

AI explanation

Using the Pythagorean theorem for the right triangle ABC, the hypotenuse BC is calculated as the square root of 6 squared plus 8 squared, which equals 10 cm. For a circle inscribed in a right triangle, the radius formula is r equals the sum of the perpendicular sides minus the hypotenuse, all divided by 2. Substituting the known values gives r equals (6 + 8 - 10) / 2, which simplifies to 4 / 2. This calculation gives a radius of 2 cm. The result is 2 cm.

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