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comp geo with rectangle and 15^o - 1998 Romania NMO VII p4

Source:

August 14, 2024
geometryrectangle

Problem Statement

Let ABCDABCD be a rectangle and let E∈(BD)E \in (BD) such that m(∠DAE)=15om( \angle DAE) =15^o. Let F∈ABF \in AB such that EF⊥ABEF \perp AB. It is known that EF=12ABEF=\frac12 AB and AD=aAD = a. Find the measure of the angle ∠EAC\angle EAC and the length of the segment (EC)(EC).
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