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Let ABC be an acute-angled triangle with AC is not equal to BC and let O be the circumcenter (of triangle ABC) and F the foot of altitude through C. Further, let X and Y be the feet of perpendiculars dropped from A and B to (the extension of) CO. Also, let M be the circumcentre of triangle FXY. Prove that M is the mid point of AB.

Let ABC be an acute-angled triangle with AC is not equal to BC and let O be the circumcenter (of triangle ABC) and F the foot of altitude through C. Further, let X and Y be the feet of perpendiculars dropped from A and B to (the extension of) CO. Also, let M be the circumcentre of triangle FXY. Prove that M is the mid point of AB.

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Grade:11

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