# Parabolas and Tangents

Geometry Level 5

Given $$\triangle ABC$$ with $$BC=28, AC=24, AB=20$$, two parabolas $$P_B, P_C$$ satisfying the following conditions are constructed:

• $$P_B$$ is tangent to segment $$AC$$ and rays $$BA,BC$$, its focus is denoted $$F_B$$

• $$P_C$$ is tangent to segment $$AB$$ and rays $$CA,CB$$, its focus is denoted $$F_C$$.

• $$F_BF_C=\frac {35}{\sqrt {3}}$$

• The axes of symmetry of the parabolas intersect at $$X$$, which lies inside the circumcircle of $$ABC$$.

Find $$\angle F_BXF_C$$ in radians

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