Problem from Euclidean Proof of Pythagoras [self-made]
Posted: Thu Apr 12, 2012 12:10 pm
Let $\bigtriangleup ABC$ has$ \angle A= \frac { \pi } {2} $.$ACC_1 A_2 $ and $BAA_1 B_1 $ both are external squares to $\bigtriangleup ABC $.$AB \cap B_1C=D_1$ and $AC \cap BC_1 =D_3$.The internal angle bisector of $ \angle BAC $ meets $BC$ at $D_2$.Prove that $AD_1D_2D_3$ is a square.
It's my one of the most favorite self-made problems.I've made its 6 different proofs.It's easy to prove it by calculation like complex,co-ordinate or by straight-cut calculation.But it can be done using only the figure!!!So I hope everyone will try to find such nice proofs.
It's my one of the most favorite self-made problems.I've made its 6 different proofs.It's easy to prove it by calculation like complex,co-ordinate or by straight-cut calculation.But it can be done using only the figure!!!So I hope everyone will try to find such nice proofs.