A triangle has corners at #(7 ,3 )#, #(2 ,5 )#, and #(1 ,4 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Area
Explanation:
Let
One solution is to determine the orthocenter
the circumcenter is the intersection of the line segment bisectors of the side AB and side AC which have the midpoints at
the equation of the line segment bisector at AB is
simplified
the equation of the line segment bisector at AC is
simplified
simultaneous solution using
Solve for R now, using any vertex of the triangle ...
let us choose A(1, 4)
it follows ,....the area of the circle with center (53/14, 31/14) radius R (see the orange line segment)
God bless....I hope the explanation is useful.