MathDB
line passes through incenter iff side equation holds

Source: Bulgaria 1973 P5

June 20, 2021
geometryincenter

Problem Statement

Let the line ℓ\ell intersects the sides AC,BCAC,BC of the triangle ABCABC respectively at the points EE and FF. Prove that the line ℓ\ell is passing through the incenter of the triangle ABCABC if and only if the following equality is true: BC⋅AECE+AC⋅BFCF=AB.BC\cdot\frac{AE}{CE}+AC\cdot\frac{BF}{CF}=AB.
H. Lesov
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