ABC is a triangle right-angled at B with perimeter 24 cm and sum of perpendicular sides minus hypotenuse = 4 cm. A circle is inscribed in the triangle. What is its radius?
A.1 cm
B.1·5 cm
C.2 cm✓ Correct
D.2·5 cm
Explanation
From previous problem, a + b = 14, c = 10, area = 24. Semi-perimeter s = 12. Inradius r = area/s = 24/12 = 2 cm. Alternatively for right triangle, r = (a + b - c)/2 = (14 - 10)/2 = 2 cm.
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