# A triangle has corners at #(5 ,6 )#, #(1 ,3 )#, and #(6 ,5 )#. What is the area of the triangle's circumscribed circle?

Area of Circumcircle

Slope of AB = (y2-y1) / (x2-x1) = (3-6) / (1-5) = 3/4#

Slope of

Cordinates of

Equation of

Slope of BC = (y2-y1) / (x2-x1) = (5-3) / (6-1) = 2/5#

Slope of

Cordinates of

Equation of

Solving Eqns (1), (2), we get circumcenter coordinates.

Radius of circumcenter R is the distance between the circumecenter O and any one of the vertices.

Area of Circumcircle

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To find the area of the circumscribed circle of a triangle, we need to determine the radius of the circle first, which is the distance from the circumcenter (center of the circumscribed circle) to any of the triangle's vertices. Then, we can use the formula for the area of a circle ((A = \pi r^2)) to find the area of the circumscribed circle.

Would you like assistance in finding the circumcenter and subsequently calculating the radius and area of the circumscribed circle?

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