A triangle has corners at (3 , 5 ), (4 ,7 ), and (8 ,6 ). What is the radius of the triangle's inscribed circle?

1 Answer
sankarankalyanam
Oct 9, 2017

Coordinates of incenter are (4.42, 6.09)

Explanation:

Let BC = a, AB = c, CA = b & Perimeter = p;
Let the incenter point be O.
a=sqrt((3-4)^2+(5-7)^2)=sqrt5=2.236
b=sqrt((8-4)^2+(6-7)^2)=sqrt17=4.123
c=sqrt((8-3)^2+(6-5)^2)=sqrt26=5.099

p=sqrt5+sqrt17+sqrt26=2.236+4.123+5.099=11.458

Ox=(aAx+bBx+cCx)/p
Ox=((2.236*8)+(4.123*3)+(5.099*4))/11.458
Ox=(17.888+12.369+20.396)/11.458= 4.421

Oy=(aAy+bBy+cCy)/p
Oy=((2.236*6)+(4.123*5)+(5.099*7))/11.458
Oy=(13.416+20.615+35.693)/11.458= 6.085
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