MathDB

5

Part of 2013 Serbia National Math Olympiad

Problems(1)

Circle through A' and B' touching AB; equal areas

Source: Serbian National Olympiad 2013, Problem 5

4/8/2013
Let A′A' and B′B' be feet of altitudes from AA and BB, respectively, in acute-angled triangle ABCABC (AC≠BCAC\not = BC). Circle kk contains points A′A' and B′B' and touches segment ABAB in DD. If triangles ADA′ADA' and BDB′BDB' have the same area, prove that ∠A′DB′=∠ACB.\angle A'DB'= \angle ACB.
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