A triangle has corners at (4,5), (1,3), and (3,3). What is the radius of the triangle's inscribed circle?

1 Answer
Kalyanam S.
Jul 29, 2018

Radius of in-circle =r=Ats=23.9208≈0.5101

Explanation:

A(4,5),B(13),C(3,3)

c=√(4−1)2+(5−3)2≈√13

a=√(1−3)2+(3−3)2≈2

b=√(3−4)2+(3−5)2≈√5

Semi perimeter s=a+b+c2

s=√13+2+√52=3.9208

Area of triangle At=√s(s−a)(s−b)(s−c), using Heron's formula

At=√3.9208(3.9208−√13)(3.9208−2)(3.9208−√5)≈2

Radius of in-circle =r=Ats=23.9208≈0.5101

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