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:

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

$s~~9.34$

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

$r~~1.28$

$A=pir^2$

$A=pi(1.28)^2$

$A~~5.15$

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