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October 29, 2018

RMO 2018 Tamil Nadu Problem 1 - angle bisector

RMO 2018 Tamil Nadu Problem 1 is from Geometry. We present sequential hints for this problem. Do not read all hints at one go. Try it yourself.

Problem

Let ABC be an acute-angled triangle and let D be an interior point of the line segment BC. Let the circumcircle of triangle ACD intersect AB at E (E between A and B) and let the circumcircle of triangle ABD intersect AC at F (F between A and C). Let O be the circumcenter triangle AEF. Prove that OD bisects ( \angle EDF )

Key ideas you will need to solve this problem

Properties of Cyclic Quadrilaterals:

Opposite angles of a cyclic quadrilateral adds up to \( 180^o \)

Angle at the center is twice the angle at the circumference.

Angles subtended by the same arc at circumference are equal.

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