# 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**