In ΔABC, ∠A = 52° and O is the orthocentre 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:

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& \angle BOC=180^{\circ }-52^{\circ }=128^{\circ }\\ & \angle BPC=90^{\circ }+\frac{\angle BOC}{2}\\ & =90^{\circ }+\frac{128}{2}\\ & =90^{\circ }+64^{\circ }\\ & =154^{\circ }\end{array}$$