A triangle has corners at #(1 , 2 )#, #(5 ,7 )#, and #(9 ,5 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-04-09T09:35:32

Radius of inscribed circle #r=1.44187#

Let #A(x_a, y_a)=(1, 2)#
Let #B(x_b, y_b)=(5, 7)#
Let #C(x_c, y_c)=(9, 5)#

Let #a# the side from B to C
Let #b# the side from A to C
Let #c# the side from A to B

#a=sqrt((x_b-x_c)^2+(y_b-y_c)^2)#
#a=sqrt((5-9)^2+(7-5)^2)=sqrt20#

#b=sqrt((x_a-x_c)^2+(y_a-y_c)^2)#
#b=sqrt((1-9)^2+(2-5)^2)#
#b=sqrt(73)#

#c=sqrt((x_b-x_a)^2+(y_b-y_a)^2)#
#c=sqrt((5-1)^2+(7-2)^2)#
#c=sqrt(41)#

Compute half of the perimeter #s#
#s=(a+b+c)/2#
#s=9.709631968875#

Compute radius #r# of inscribed circle

#r=sqrt(((s-a)(s-b)(s-c))/s)#
#r=1.44187#

God bless....I hope the explanation is useful.