A triangle has corners at #(9 ,3 )#, #(4 ,6 )#, and #(2 ,4 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Solving Eqns (1), (2), we get the circum centerr O
Area of the circum-circle
Explanation:
Slope of line segment
Slope of perpendicular bisector passing through F
Mid point of DC = F has coordinates
#F ( (4+2)/2, (6+4)/2) = F(3,5)
Equation of FO where O is the circumcenter
Slope of line segment
Slope of perpendicular bisector passing through B
Mid point of AD = B has coordinates
#B ( (9+4)/2, (3+6)/2) = F(13/2,9/2)
Equation of BO where O is the circumcenter
Solving Eqns (1), (2), we get the coordinates of circum centerr O
we can get the radius of the circum-circle by finding the distance of O from any one of the three vertices.
Area of circum-circle