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perpendicular inside a right triangle, altitude and midpoints

Source: 2006 Indonedia MO Province P2 q1 OSP

December 11, 2020
geometryperpendicularright triangle

Problem Statement

Suppose triangle ABCABC is right-angled at BB. The altitude from BB intersects the side ACAC at point DD. If points EE and FF are the midpoints of BDBD and CDCD, prove that AE⊥BFAE \perp BF.
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