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About LinkBacksin triangle ABC The point P lies on the side BC so that AB+BP=AC+CP ,and the point Q lies on the side AC so that:BA+AQ=BC+CQ and the point R lies on the side AB so that:CB+BR=CA+AR .How to prove that the lines AP,BQ,CR are meet
in triangle ABC The point P lies on the side BC so that AB+BP=AC+CP ,and the point Q lies on the side AC so that:BA+AQ=BC+CQ and the point R lies on the side AB so that:CB+BR=CA+AR .How to prove that the lines AP,BQ,CR are meet
Suppose AR = a, RB = b, BP = c, PC = d, CQ = e, QA = f. From the conditions of the problem, we know that
(1)
(2)
(3)
Subtracting (2) from (1), we obtain. Subtracting (3) from (2),
. Plugging this back into (1), we obtain
.
Therefore. The segments AP, BQ, CR must intersect at a point, due to Ceva's theorem.
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