A triangle has corners at #(3 ,8 )#, #(5 ,9 )#, and #(4 ,5 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Explanation:
We need to find the radius
Using the distance formula we get three equations
The first two of these give us
and the last two
(You could try to form another of these by taking the first and the third, but that one will turn out to be equivalent to these two)
Changing sides and using
This pair of linear simultaneous equations can be solved easily to yield
Substituting these in any of the first three equations will give us
and the area of the circumscribed circle is simply