Multiple choice

A circle is inscribed in a triangle with sides 9, 12, and 15. The radius of the circle is

  1. 2

  2. 3

  3. 3.5

  4. 4

  5. 4.6
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B Correct answer
Explanation

The triangle is a right-angled triangle (9^2 + 12^2 = 81 + 144 = 225 = 15^2). The inradius of a right triangle is (a+b-c)/2 = (9+12-15)/2 = 6/2 = 3.

AI explanation

The given side lengths of 9, 12, and 15 satisfy the Pythagorean theorem (9^2 + 12^2 = 15^2), so the triangle is a right-angled triangle with the hypotenuse as its diameter. The radius of a circle inscribed in a right triangle is given by the formula r = (a + b - c) / 2, where a and b are the legs and c is the hypotenuse. Substituting the values gives r = (9 + 12 - 15) / 2 = 6 / 2 = 3. The radius of the inscribed circle is 3.

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