Prove that triangle is isosceles, triangle that is inscribed in a circle. $AD$ is a median to side $BC$ in triangle $ABC$ that is inscribed in a circle that his center is in $(5,6)$.
Given: $ D (9,2)$ and the centroid of the triangle is $(6,5$).
There is not so much information given about the circle, thus I can't draw very good the circle (for example I don't know points in the circle, a point of the triangle or radius of the circle). There is my problem. I feel I have few given information and don't know how to start.
Can someone help me how to prove that ABC is isosceles?

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*Loacte O(5, 6), G(6, 5), D(9,2).





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*Form the equation of GD. O is found to be a point on GD.

*Since ADG is a median, A must be on DG extended. From the fact that AG = 2GD. Point A is fixed.

*Draw the circum-circle (centered at O with radius OA).

*Since B and C must lie on the circum-circle of ABC, BC is a chord of that circle with D as its midpoint. Note that OD is the line from center joining the midpoint of the chord BC. This makes OD the perpendicular bisector of BC. We can therefore locate B and C.
Point 4 above also supplies enough information to conclude $\triangle ABC$ is isosceles. 
