Multiple choice

A circle with centre O is inscribed in a right angle triangle ABC, right angled at B. If BC = 15 cm, AC = 17 cm, the radius 'r' of the circle is:

  1. 2 cm

  2. 2.5 cm

  3. 3 cm

  4. 5 cm
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C Correct answer
Explanation

In a right triangle with sides 15 and 17, the third side is sqrt(17^2 - 15^2) = sqrt(289 - 225) = sqrt(64) = 8. The radius of the inscribed circle in a right triangle is r = (a + b - c) / 2, where a and b are legs and c is the hypotenuse. r = (8 + 15 - 17) / 2 = 6 / 2 = 3 cm.

AI explanation

Using the Pythagorean theorem for the right triangle ABC, the side AB is calculated as the square root of (17 squared minus 15 squared), which equals the square root of 64, giving AB as 8 cm. The radius of an incircle in a right triangle can be found using the formula r equals the sum of the perpendicular sides minus the hypotenuse, all divided by 2. Substituting the known values into the formula gives r equals 8 plus 15 minus 17, divided by 2, which simplifies to 6 divided by 2, resulting in a radius of 3 cm. The radius is 3 cm.

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