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Determine CE if AC=7 and CB=4

Source: Baltic Way 1995

October 8, 2011
geometry proposedgeometry

Problem Statement

In the triangle ABCABC, let ℓ\ell be the bisector of the external angle at CC. The line through the midpoint OO of ABAB parallel to ℓ\ell meets ACAC at EE. Determine ∣CE∣|CE|, if ∣AC∣=7|AC|=7 and ∣CB∣=4|CB|=4.
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