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Parallel Midpoints (Posted on 2016-07-30) Difficulty: 4 of 5

Let BD be an altitude of ΔABC with D between A and C (not the midpoint).
The bisector of ∠ACB intersects BD and AB in points P
and Q respectively. The bisector of ∠CAB intersects BD
and BC in points R and S respectively. F and G are the
midpoints of PQ and RS respectively.

Prove that FG is parallel with AC if and only if ∠ABC = 90°.

See The Solution Submitted by Bractals    
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  Subject Author Date
not full solutionarmando2016-08-03 09:58:40
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