# Projections of Midpoints onto Circumradii

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Let ABC be an acute triangle with circumcenter O, circumradius , and inradius . Let A', B', and C' be the midpoints of BC, AC, and AB, respectively. Let D, D' be the projections of A' onto the circumradii OB and OC. Define E, E' and F, F' similarly for the points B' and C'. Then .

Contributed by: Jay Warendorff (March 2011)

Open content licensed under CC BY-NC-SA

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See problem 62 in N. Altshiller-Court, *College Geometry*, 2nd ed., Mineola, NY: Dover, 2007 p. 119.

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