Multiple choice

A circle is inscribed in a right-angled triangle with legs measuring 6 cm and 8 cm. What is the radius of the inscribed circle?

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. 5 cm

  5. 6 cm
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A Correct answer
Explanation

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

AI explanation

Using the formula for the inradius of a right-angled triangle, the radius is the sum of the legs minus the hypotenuse, all divided by 2. First, the hypotenuse is the square root of 6 squared plus 8 squared, which is the square root of 100, or 10 cm. Applying the formula, the radius is 6 plus 8 minus 10, divided by 2, resulting in a radius of 2 cm.

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