In ΔABC, ∠A = 52° and O is the orthocenter of the triangle (BO and CO meet AC and AB at E and F respectively when produced). If the bisectors of ∠OBC and ∠OCB meet at P, then the measure of ∠BPC is ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 154°.
∠COB = ∠EOF = 180° - 52°
⇒ ∠COB = 128°
∠BPC = 90° + (∠COB/2)
⇒ ∠BPC = 90° + 128/2 = 90 + 64 = 154°