Let AC be a line segment in the plane and B a point between A and C. Construct isosceles triangles PAB and QBC on one side of the segment AC such that ∠APB = ∠BQC = 120 and an isosceles triangle RAC on the other side of AC such that ∠ARC = 120. Show that PQR is an equilateral triangle
This question can be solved in two different methods. Method 1: Drop perpendiculars from P and Q to AC and extend them to meet AR,RC in K,L respectively. Join KB,PB,QB,LB,KL. Refer to fig.1 Method 2
Introduction of Mathematical Olympiad
The Mathematical Olympiad programme consists of six stages. Stage 1 The first stage examination, the Pre-Regional Mathematics Olympiad (PRMO) is a three-hour examination with 30 questions. The answer to each question is either a single-digit number of a two-digit number and will need to be marked on a machine-readable OMR response sheet. The PRMO question … Continue reading Introduction of Mathematical Olympiad
M CUBE: MatheMatics by Maheshwari 