A triangle has corners at #(7 ,5 )#, #(2 ,3 )#, and #(1 ,4 )#. What is the area of the triangle's circumscribed circle?
1 Answer
The area of the circumscribed circle is:
Explanation:
The standard Cartesian form of the equation of a circle is:
where
When I do a problem of this type, I shift all 3 points so that one point is then origin,
Use equation [1] and the new points to write 3 equation:
Equation [2] simplifies into:
Substitute the left side of equation [5] into the right sides of equations [3] and [4]:
Expand the squares:
The
Collect the constant terms into a single term on the right:
Multiply equation [10] by -2 and add to equation [11]:
Substitute #25/14 for h in equation [10] and the solve for k:
Substitute the values for h and k into equation [5]
The area of a circle is:
The area of the circumscribed circle is: