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symmedian ratio

Source: 2023 Viet Nam math olympiad for high school students D1 P1

March 25, 2023
geometry

Problem Statement

Given a triangle ABCABC with ADAD is the A−A-symmedian (D(D is on the side BC).BC).
Prove that: DBDC=AB2AC2.\dfrac{DB}{DC}=\dfrac{AB^2}{AC^2}.
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