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<FCE=? <FEC=< CEB$ , < DFC=< CFE in rectangle ABCD

Source: 2022 2nd OMpD L2 P2 - Brazil - Olimpíada Matemáticos por Diversão

October 13, 2022
geometryrectangleequal anglesangles

Problem Statement

Let ABCDABCD be a rectangle. The point EE lies on side AB‾ \overline{AB} and the point FF is lies side AD‾ \overline{AD}, such that ∠FEC=∠CEB\angle FEC=\angle CEB and ∠DFC=∠CFE\angle DFC=\angle CFE. Determine the measure of the angle ∠FCE\angle FCE and the ratio AD/ABAD/AB.
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