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2018 preRMO p10, (BC^2 + CA^2 + AB^2)/100, perp. medians

Source:

August 8, 2019
mediangeometryperpendicular

Problem Statement

In a triangle ABCABC, the median from BB to CACA is perpendicular to the median from CC to ABAB. If the median from AA to BCBC is 3030, determine BC2+CA2+AB2100\frac{BC^2 + CA^2 + AB^2}{100}.
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