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MathNet 2011 Question 23

Math Olympiad Vault · MathNet 2011

Question 23

Let $ABC$ be a triangle, and let $D$, $E$, and $F$ be the midpoints of sides $BC$, $CA$, and $AB$, respectively. Let the angle bisectors of $\angle FDE$ and $\angle FBD$ meet at $P$. Given that $\angle BAC = 37^{\circ}$ and $\angle CBA = 85^{\circ}$, determine the degree measure of $\angle BPD$.