A Triangle Area from Three Interior Distances

★ 8/10plane geometry Quadratic Equations analytic geometry Triangle Geometry

Problem

In $\triangle ABC$ , $AB=2AC$ and $\angle BAC=60^\circ$ . An interior point $P$ satisfies $PA=\sqrt 3$ , $PC=2$ , $PB=5$ . Find the area of $\triangle ABC$ .

Answer

Solution

Difficulty	8/10
Topics	plane geometry, Quadratic Equations, analytic geometry, Triangle Geometry

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