A triangle has corners at #(4 ,7 )#, #(8 ,9 )#, and #(3 ,5 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Explanation:
Let's subtract 3 from every x coordinate and 5 from every y coordinate; this will make the 3rd point the origin.
We do this because we are going to use the standard form of the equation of a circle:
and the 3 points to write 3 equations. This makes the equation for the point that is the origin very simple and useful:
Substitute the left side of equation [1] into equations [2] and [3]:
Expand the squares:
The square terms cancel:
Remove all of the cancelled terms and collect the constants on the right:
Multiply equation [8] by -2 and add to equation [9]:
Substitute into equation [9]:
Use equation [1] to find the value of
The area of the circle is: