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RMO KV 2024 Q3

Source: RMO KV 2024 Q3

November 3, 2024
geometryperpendicular bisector

Problem Statement

Let ABCABC be an equilateral triangle. Suppose DD is the point on BCBC such that BD+DC=1:3BD+DC = 1:3. Let the perpendicular bisector of ADAD intersect AB,ACAB,AC at E,FE,F respectively. Prove that 49⋅[BDE]=25⋅[CDF]49 \cdot [BDE] = 25 \cdot [CDF], where [XYZ][XYZ] denotes the area of the triangle XYZXYZ.
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