A triangle has sides with lengths of 2, 7, and 6. What is the radius of the triangles inscribed circle?

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Answer 1 · 2018-07-29T14:45:49

In-circle radius #color(brown)(r = A_t / s ~~ 0.7416# units.

Lengths of sides #a = 2, b = 7, c = 6#

In-circle radius #r = A_t / s#

Semi perimeter of triangle #s = (a + b + c)/2 = (2+7+6)/2 = 7.5# units

Area of triangle #A_t = sqrt(s (s-a) (s-b) (s-c))#, using Heron’s formula.

#A_t = (7.5 (7.5-2) (7.5-7) (7.5-6)) = 5.5621# sq. units

In-circle radius #color(brown)(r = A_t / s = 5.5621 / 7.5 ~~ 0.7416# units.