Maths Olympiad Exam

Let ABC be a triangle in which A = 60. Let BE and CF be the bisectors of the angles B and C with E on AC and F on AB. Let M be the reflection of A in the line EF. Prove that M lies on BC.

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Maths Olympiad Other Question

Find three distinct positive integers with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer. Let ABC be a triangle in which AB = AC and let I be its in-centre. Suppose
BC = AB + AI. Find BAC.