A right-angled triangle has legs 6 cm and 8 cm and hypotenuse 10 cm. A circle drawn outside the triangle touches the hypotenuse and also touches both legs extended beyond the hypotenuse (on the side away from the right angle). What is the radius of this circle?

Question

Accepted Answer

12 cm. This is the escribed circle opposite the right angle, whose radius is r = area/(s − c), where c is the side it touches. Area = ½ × 6 × 8 = 24 and s = (6 + 8 + 10)/2 = 12, so r = 24/(12 − 10) = 12 cm. (Using s alone in the denominator would wrongly give the inradius 2 cm.)

A right-angled triangle has legs 6 cm and 8 cm and hypotenuse 10 cm. A circle drawn outside the triangle touches the hypotenuse and also touches both legs extended beyond the hypotenuse (on the side away from the right angle). What is the radius of this circle?

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