Multiple choice

A circle is inscribed in a triangle with sides $8,15 and 17$. The radius of the circle is.

  1. $6$
  2. $2$
  3. $5$
  4. $3$
  5. $7$
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D Correct answer
Explanation

The triangle with sides 8, 15, 17 is a right-angled triangle (8^2 + 15^2 = 64 + 225 = 289 = 17^2). The inradius of a right triangle is (a + b - c) / 2 = (8 + 15 - 17) / 2 = 6 / 2 = 3.

AI explanation

The given side lengths 8, 15, and 17 form a right-angled triangle since 8 squared plus 15 squared equals 17 squared. The area is half of 8 times 15, which is 60, and the semi-perimeter is 8 plus 15 plus 17 divided by 2, resulting in 20. Using the formula for the inradius of a right triangle, r equals the area divided by the semi-perimeter, we get 60 divided by 20, which is 3.

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