Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemClick the figure below to see the complete problem 503 about Triangle with Three Squares, Perpendicular, Congruence, Concurrency.
There is a minor typo error in my previous comment. Below is the corrected copyCall Q the projection of M over ABWe have QM=QB and ang (MQB)=90And QO=QN and ang ( OQN)=90 ( See Problem 497)Triangle MQN congruence with tri. BQO (case SAS)Tri. MQN is the image of Tri. QBO in the rotational transformation of center Q and angle of rotational=90So MN=BO and MN perpen. To BO.With same reason as above we also have MP perpen. To NO and AM perpen. To MO.P is the orthocenter of triangle MNO . AN, BO and CM concurrence at PPeter Tran