A triangle has corners at $(6 ,4 )$ , $(7 ,6 )$ , and $(3 ,8 )$ . What is the area of the triangle's circumscribed circle?

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Answer 1 · 2018-02-02T12:29:49

Area of triangle's circumscribed circle is $19.63$ sq.unit.

Vertices of triangle are $A(6,4), B(7,6) , (3,8)$

Side $AB=a=sqrt((6-7)^2+(4-6)^2)=sqrt5 ~~2.24$

Side $BC=b=sqrt((7-3)^2+(6-8)^2)= sqrt20 ~~ 4.47$

Side $CA=c=sqrt((3-6)^2+(8-4)^2)=sqrt 25 = 5.0$

Semi perimeter of triangle $S=(2.24+4.47+5.0)/2=5.855$

Area of the triangle $A_t=sqrt(s(s-a)(s-b)(s-c))$

$=sqrt(5.555(5.855-2.24)(5.855-4.47)(5.855-5.0))$

$= sqrt25.06 ~~5.0$ sq.unit.

Circumscribed circle radius is $R=(a*b*c)/(4.A_t)$

$R=(2.24*4.47*5.0)/(4*5.0) ~~ 2.5$ unit

Area of circumscribed circle is $A_c =pi*R^2=pi*2.5^2~~19.63$ .

Area of circumscribed circle is $19.63$ sq.unit. [Ans]

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