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Putnam 1999 B1

Source:

December 22, 2012
Putnamlimittrigonometrycollege contests

Problem Statement

Right triangle ABCABC has right angle at CC and ∠BAC=θ\angle BAC=\theta; the point DD is chosen on ABAB so that ∣AC∣=∣AD∣=1|AC|=|AD|=1; the point EE is chosen on BCBC so that ∠CDE=θ\angle CDE=\theta. The perpendicular to BCBC at EE meets ABAB at FF. Evaluate lim⁡θ→0∣EF∣\lim_{\theta\to 0}|EF|.
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