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2017 IGO Intermediate P1

Source: 4th Iranian Geometry Olympiad (Intermediate) P1

September 15, 2017
IGOIrangeometry

Problem Statement

Let ABCABC be an acute-angled triangle with A=60∘A=60^{\circ}. Let E,FE,F be the feet of altitudes through B,CB,C respectively. Prove that CE−BF=32(AC−AB)CE-BF=\tfrac{3}{2}(AC-AB)
Proposed by Fatemeh Sajadi
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