An Incenter Times a Foot

★ 8/10plane geometry Reflection Tangent Circle conic sections Triangle Geometry

Problem

The point $P$ lies on the right branch of $x^2 - \dfrac{y^2}{3} = 1$ with foci $F_1, F_2$ , and $|PF_2| = 2$ . Let $I$ be the incenter of $\triangle PF_1F_2$ , $O$ the origin, and $M$ the foot of the perpendicular from $F_1$ to line $PI$ . Find $|OI| \cdot |OM|$ .

Answer

Solution

Difficulty	8/10
Topics	plane geometry, Reflection, Tangent Circle, conic sections, Triangle Geometry

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