Multiple choice

In $\triangle ABC$, $\overline {AC}$ = 24 cm, $\overline{BC}$ = 10 cm, and $\overline {AB}$ = 26 cm. The radius of the inscribed circle is:

  1. 26 cm

  2. 4 cm

  3. 13 cm

  4. 8 cm
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B Correct answer
Explanation

The sides are 10, 24, 26. Since 10^2 + 24^2 = 26^2, it is a right triangle. The inradius r = (a + b - c) / 2 = (10 + 24 - 26) / 2 = 8 / 2 = 4.

AI explanation

The sides 10 cm, 24 cm, and 26 cm form a right-angled triangle because 10 squared plus 24 squared equals 26 squared. The area is half of 10 times 24, which is 120 square cm, and the semi-perimeter is 10 plus 24 plus 26 divided by 2, giving 30 cm. Using the inradius formula r equals Area divided by s, we calculate 120 divided by 30, which results in a radius of 4 cm.

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