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ABC is a right triangle with the right angle at A. A circle is inscribed in the triangle. If the two legs containing the right angle are 6 cm and 8 cm, find the radius of the inscribed circle.

1. 2 cm
2. 1 cm
3. 3 cm
4. 2.5 cm

Correct answer: 2 cm

Solution

Legs 6 and 8, hypotenuse = sqrt(36 + 64) = 10. For a right triangle, r = (leg1 + leg2 - hypotenuse)/2 = (6 + 8 - 10)/2 = 4/2 = 2 cm. (Equivalently r = area/s = 24/12 = 2.)

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