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| Sum of Chords (Posted on 2013-09-07) |
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Point P lies on the circumcircle of equilateral
triangle ABC in the
interior of ∠BAC.
Prove that |AP| = |BP| + |CP|.
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Submitted by Bractals
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Solution:
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Apply Ptolemy's theorem to the cyclic quadrilateral ABPC,
|AP||BC| = |BP||AC| + |CP||AB|.
Cancel equal quantities |BC|, |AC|, and |AB|,
|AP| = |BP| + |CP|.
QED
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Subject |
Author |
Date |
 | Solution | Jer | 2013-09-07 13:30:53 |
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