Geometry Problem
Click the figure below to see the complete problem 503 about Triangle with Three Squares, Perpendicular, Congruence, Concurrency.
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Complete Problem 503
Level: High School, SAT Prep, College geometry
Sunday, August 15, 2010
Problem 503: Triangle with Three Squares, Perpendicular, Congruence, Concurrency
See also:
Complete Problem 503
Level: High School, SAT Prep, College geometry
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There is a minor typo error in my previous comment. Below is the corrected copy
ReplyDeleteCall Q the projection of M over AB
We have QM=QB and ang (MQB)=90
And 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=90
So 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 P
Peter Tran