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What is the radius of the circle inscribed in triangle $ABC$ if $AB = 15,$ $AC = 41,$ and $BC = 52$?

Feb 26, 2021

#1
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A = rs

semiperimeter = s = (15 + 41 + 52)/2 = 54

area = A = $$\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{(54)(2)(39)(13)} = 234$$

radius = r = $$\frac{A}{s} = \frac{234}{54} = \frac{13}{3}$$

Feb 26, 2021