21st CanMO 1989 Problem 2 Each vertex of a right angle triangle of area 1 is reflected in the opposite side. What is the area of the triangle formed by the three reflected points? Solution
: 3. Let the original triangle be ABC with angle B = 90 o . Let the reflection of A be A' and so on. Then ABA' and CBC' are straight lines and B is the midpoint of AA' and CC'. So C'A' is parallel to AC and of equal length. Also BB' is perpendicular to AC and to C'A'. Hence the altitude from B' to C'A' is three times the length of the altitude from B to AC. So the area of A'B'C' is three times that of ABC. 21st CanMO 1989 © John Scholes jscholes@kalva.demon.co.uk 21 June 2002