Q1)Let ABC be a triangle in which ∠A = \(60^ {\circ}\) 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.

Q2) Let ABCD be a convex quadrilateral. Let E, F, G, H be midpoints of AB, BC, CD, DA respectively. If AC, BD, EG, FH concur at a point O, prove that ABCD is a parallelogram.

Q3) (Extra one) Let ABC be an acute angled scalene triangle with circumcenter O and orthocenter H. If M is the midpoint of BC, then show that AO and HM intersect at the circumcircle of ABC.

(Problems taken from previous year RMO papers)

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