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sum AA_2/ AA_1=4, altitude, circumcircle 2014-15 Dürer Round1 D4

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December 5, 2022
geometrycircumcirclealtitudeDurer

Problem Statement

The altitude of the acute triangle ABCABC drawn from AA , intersects the side BCBC at A1A_1 and the circumscribed circle at A2A_2 (different from AA). Similarly, we get the points B1B_1, B2B_2, C1C_1, C2C_2. Prove that AA2AA1+BB2BB1+CC2CC1=4.\frac{AA_2}{AA_1}+\frac{BB_2}{BB_1}+\frac{CC_2}{CC_1}= 4.
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