A triangle has corners at #(2 , 9 )#, #(3 ,7 )#, and #(1 ,1 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-03-10T08:27:24

#r=0.60158" "#units

From the given data:
Let A(2, 9) and B(3,7) and C(1,1)

We let side a the distance B to C
We let side b the distance A to C
We let side c the distance A to B

Compute the lengths of the sides

#a=sqrt((x_b-x_c)^2+(y_b-y_c)^2)#
#a=sqrt((3-1)^2+(7-1)^2)#
#a=2sqrt10#

#b=sqrt((x_a-x_c)^2+(y_a-y_c)^2)#
#b=sqrt((2-1)^2+(9-1)^2)#
#b=sqrt(65)#

#c=sqrt((x_a-x_b)^2+(y_a-y_b)^2)#
#c=sqrt((2-3)^2+(9-7)^2)#
#c=sqrt((1+4)#
#c=sqrt5#

We are now ready to compute for the radius #r# of the triangle's inscribed circle:

Formula #r=sqrt(((s-a)(s-b)(s-c))/s)" " "#where #s=(a+b+c)/2#

#s=(2sqrt10+sqrt65+sqrt5)/2=8.3114405230675#

#r=#
#sqrt(((8.311440-2sqrt10)(8.311440-sqrt65)(8.311440-sqrt5))/8.311440)#

#r=0.60158" "#units

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