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

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Answer 1 · 2016-07-03T13:57:41

Area of the crcm.crcl. of #Delta=pi*R^2=25pi/4~=19.625.#

Call the vertices #A(7,4), B(3,6)# and #C(4,8).#

Let #c# denote the length of side #AB#, then, by Dist. Formula,

#c^2=(7-3)^2+(4-6)^2=16+4=20.#

Similarly, #a^2=1+4=5# and, #b^2=9+16=25#

#:. b^2=c^2+a^2#

Therefore, #DeltaABC# is a right#/_^(ed) Delta# with #b=AC# as its hypo.

Accordingly, its circumcentre is the mid-pt. #M# of hypo. #AC#, and as such, its cicm.radi. #R=b/2=5/2.#

Finally, the reqd. Area of the crcm.crcl. of #Delta ABC=pi*R^2=25pi/4~=19.625.#