A triangle has corners at #(6 ,3 )#, #(5 ,4 )#, and #(3 ,2 )#. What is the area of the triangle's circumscribed circle?

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Answer 1 · 2017-02-20T17:03:37

#2.5pi.#

Name the points #A(6,3), B(5,4) and C(3,2).#

By the Distance Formula,

#AB^2=(6-5)^2+(3-4)^2=1+1=2,#

#BC^2=4+4=8, &, AC^2=10 rArr AB^2+BC^2=AC^2.#

This means that, #Delta ABC" is a right "Delta,# having

Hypotenuse #AC.#

Knowing that, in the right #Delta#, the hypotenuse is the

circum-diameter, we find that, the cicrumradius #R# of

#DeltaABC# is, #R=(AC)/2.#

Therefore, the Area of the Circumscribed Circle of #DeltaABC#

#=piR^2=pi(AC)^2/4=pi(10/4)=2.5pi.#

Enjoy Maths.!