A triangle has corners at #(6 ,3 )#, #(5 ,8 )#, and #(4 ,2 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Shift all 3 points so that one is the origin. Use the standard Cartesian equation of a circle and the new points to write 3 equations. Solve the 3 equations for
Explanation:
Shift all three points so that one is the origin:
Use the standard Cartesian equation of a circle:
and the three new points to write 3 equations:
Expand the squares using the pattern
Subtract equation [6] from equation [4] and [5]:
Collect the constant terms into a single term on the right:
Multiply equation [9] by -6 and add to equation [10]:
Substitute
Use equation [6], to compute the value of
The formula for the area of the circle is
Substitute the value for