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Oh < 3r

Source: APMO 1994

March 11, 2006
geometrycircumcircleEuleranalytic geometryperpendicular bisectorcomplex numbersgeometry unsolved

Problem Statement

Given a nondegenerate triangle ABCABC, with circumcentre OO, orthocentre HH, and circumradius RR, prove that ∣OH∣<3R|OH| < 3R.
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