SOLUTION: In triangle ABC, the perpendiculars, AX BY and CZ drawn from the vertices A, B and C on the sides BC, CA and AB respectively meet at O. show that AO. OX = BO. OY = CO. OZ.
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Question 1077820: In triangle ABC, the perpendiculars, AX BY and CZ drawn from the vertices A, B and C on the sides BC, CA and AB respectively meet at O. show that AO. OX = BO. OY = CO. OZ.
0. Make a sketch to follow my arguments.
1. The triangles AOY and BOX are right-angled triangles.
They have congruent acute angles AOY and BOX (these angles are congruent since they are vertical).
Therefore, these triangles are SIMILAR.
It implies that the corresponding sides are proportional: = .
Hence, |AO|*|OX| = |BO|*|OY|.
2. The other equality is proved similarly.
Prove it on your own as an exercise.
