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

1 Answer
Oct 2, 2017

See the answer below...

Explanation:

Suppose the circumcentre of the triangle is (x,y)

$1st STEP$
Hence the distance of the point of the circumcentre from the corners of the triangle will be same...
So we can write ,
(x2)2+(y4)2=(x6)2+(y5)2=(x3)2+(y3)2
[Squaring each part and removing x2 and y2 from each part]

4x+48y+16=12x+3610y+25=6x+96y+9
Hence we get equations ...
i) 8x+2y=41[From 1st and 2nd equation ]
ii)6x+4y=43[From 2nd and 3rd equation]

From these equations we get
16x+4y6x4y=8243
x=3.9
Similarly we get the value of y=418×3.92=4.9

Thus we can determine the value of the radius of the circle...
(3.92)2+(4.92)2=2.1unit (approx)
Hence the area of the circle is π×r2=13.86unit2 (approx)