A triangle has corners at #(8 ,7 )#, #(2 ,1 )#, and #(3 ,6 )#. What is the area of the triangle's circumscribed circle?

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Answer 1 · 2018-06-21T15:02:17

#A~~5.15#

First we need to find the length of each side, to do this we need to use the distance formula on pairs of ordered pairs:

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d=sqrt((8-2)^2+(7-1)^2)=6sqrt2#

#d=sqrt((2-3)^2+(1-6)^2)=sqrt26#

#d=sqrt((3-8)^2+(6-7)^2)=sqrt26#

Now use the formula for a triangle inscribed circle:

#s = (a+b+c)/2#

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

Plug in our values:

#s = (6sqrt2+sqrt26+sqrt26)/2#

#s~~9.34#

#r = sqrt(((9.34-6sqrt2)(9.34-sqrt26)(9.34-sqrt26))/9.34)#

#r~~1.28#

#A=pir^2#

#A=pi(1.28)^2#

#A~~5.15#