A triangle has corners at (9,1), (4,6), and (7,4). What is the area of the triangle's circumscribed circle?

1 Answer
Douglas K.
Dec 24, 2017

Area=169π2

Explanation:

One way to solve this problem is as follows.

The vertices of the triangle are, also, points on the circumscribed circle; this allow us to use the Cartesian equation for a circle, (x−h)2+(y−k)2=r2, and the 3 given (x,y) points, (9,1),(4,6),and(7,4) to write 3 equations:

(9−h)2+(1−k)2=r2 [1]
(4−h)2+(6−k)2=r2 [2]
(7−h)2+(4−k)2=r2 [3]

where (h,k) is the center of the circumscribed circle and r is its radius.

After a lot of non-linear algebra, you can verify that r=13√2

The formula for the area of the circumscribed circle is:

Area=πr2

Substitute r=13√2:

Area=169π2

Related questions
See all questions in Area of Inscribed Triangle
Impact of this question
1221 views around the world
You can reuse this answer
Creative Commons License