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| Parallel Bisections (Posted on 2006-11-27) |
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In triangle ABC, the perpendiculars from A to the internal bisectors of angles B and C meet those bisectors at X and Y. Prove that XY is parallel to BC.
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Submitted by Bractals
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Rating: 1.0000 (1 votes)
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Solution:
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Extend the rays AX and AY to intersect line BC at points X' and Y' respectively. Right triangles BXA and BXX' are congruent as are right triangles CYA and CYY'. Therefore, X and Y are the midpoints of sides AX' and AY' of triangle AX'Y'. Thus, XY is parallel to X'Y' and hence to BC.
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