An Apollonius Maximum

★ 8/10plane geometry trigonometry Apollonius Circle Triangle Geometry

Problem

In triangle $ABE$ , points $C$ and $D$ lie on segment $BE$ with $BE = 3$ , $\angle BAC = \angle EAD$ , and

\frac{BC \cdot BD}{DE \cdot EC} = \frac{1}{4}.

When $\angle AEB$ attains its maximum value, find the area of triangle $ABE$ .

Answer

Solution

Difficulty	8/10
Topics	plane geometry, trigonometry, Apollonius Circle, Triangle Geometry

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