4th Mexico 1990 Problem A2 ABC is a triangle with ∠B = 90 o and altitude BH. The inradii of ABC, ABH, CBH are r, r 1 , r 2 . Find a relation between them.
r 2 = r 1 2 + r 2 2 Solution The triangles are similar so r: r 1 : r 2 = AC : AB : BC. Hence r 2 = r 1 2 + r 2 2 . 4th Mexican 1990 © John Scholes jscholes@kalva.demon.co.uk 28 February 2004 Last corrected/updated 28 Feb 04