A triangle has corners at #(9 ,4 )#, #(2 ,5 )#, and #(3 ,6 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Explanation:
I always begin this type of problem by shifting all 3 points so that one of them is the origin. Let's shift
I do this, because I am going use the standard equation of a circle:
to write 3 equations using the points. Because the first point is the origin, equation is simplified to become:
We can use equation [1] to substitute
Expand the left sides of equations [4] and [5]:
cancel the square terms:
Collect the constant terms on the right:
Add equation [8] to equation [9]:
A simplified version of equation [9] will help us find the value k:
Use equation [1] to find the value of
The area of the circle is: