A triangle has corners at #(8 ,1 )#, #(4 ,5 )#, and #(6 ,7 )#. What is the area of the triangle's circumscribed circle?
2 Answers
Area of triangle's circumscribed circle is
Explanation:
The three corners are
Distance between two points
Side
Side
Side
Area of Triangle is
Radius of circumscribed circle is
Area of triangle's circumscribed circle is
Area of circumcircle
Explanation:
Refer figure abov.
B is mid point of AB
Coordinates of
Similarly coordinates of
Slope of AD
Slope of perpendicular line through B
Eqn of perpendicular line through B is
Slope of CD
Slope of perpendicular line through F
Eqn of perpendicular line through F is
Solving Eqns (1), (2) we get the coordinates of circumcenter O.
Radius of circumcircle is distance of O from the vertices A, D or C.
I.e
Area of circumcircle