Practice problems
Q1. If the medians BE and CF are equal in a △ABC prove that AB=AC. S1. Let G be the centroid and let CG = 2x = BG. Let EG = FG = x. Now triangles EGC and FGB are congruent by SAS. Why? Since EG = FG, CG = BG and angle FGB = angle CGE because they are vertical angles. => FB = EC And BF = FA since F is midpoint of AB, similarly AE = EC. => AF + FB = AE + EC => AB = AC H.P. Q2. Let (D, E, F) be the feet of the altitude from (A, B, C) in a (\triangle ABC). Prove that the perpendicular bisector of (EF) also bisects (BC). S2. BCEF is a cyclic quadrilateral with BC as diameter. Perpendicular bisector of EF will pass through the center of the circle since EF is a chord. Center lies on the midpoint of BC as it is a diameter. Hence perpendicular bisector of EF will pass through the midpoint of BC. H.P. Q3. If S S is the circumcentre of a △ A B C △ A BC and D , E , F D , E , F are the feet of the altitudes of △ A B C △ A BC th...