MathNet 2008-part-05 — 164 problems (EN–VI) Question 102

In a triangle $ABC$, take point $D$ on $BC$ such that $DB = 14$, $DA = 13$, $DC = 4$, and the circumcircle of $ADB$ is congruent to the circumcircle of $ADC$. What is the area of triangle $ABC$?