MathDB
2009 ToT Spring Junior A P7 sum of triangle areas

Source:

February 26, 2020
isoscelesgeometryareas

Problem Statement

Angle CC of an isosceles triangle ABCABC equals 120o120^o. Each of two rays emitting from vertex CC (inwards the triangle) meets ABAB at some point (PiP_i) reflects according to the rule the angle of incidence equals the angle of reflection" and meets lateral side of triangle ABCABC at point QiQ_i (i=1,2i = 1,2). Given that angle between the rays equals 60o60^o, prove that area of triangle P1CP2P_1CP_2 equals the sum of areas of triangles AQ1P1AQ_1P_1 and BQ2P2BQ_2P_2 (AP1<AP2AP_1 < AP_2).