MathDB

3

Part of 2008 Hong kong National Olympiad

Problems(1)

Prove H is the orthocentre from given condition

Source: 11th CHKMO 2009

12/15/2008
ΔABC \Delta ABC is a triangle such that AB≠AC AB \neq AC. The incircle of ΔABC \Delta ABC touches BC,CA,AB BC, CA, AB at D,E,F D, E, F respectively. H H is a point on the segment EF EF such that DH⊥EF DH \bot EF. Suppose AH⊥BC AH \bot BC, prove that H H is the orthocentre of ΔABC \Delta ABC. Remark: the original question has missed the condition AB≠AC AB \neq AC
geometrytrigonometryratioincenterinradiuscircumcircleparallelogram