Question 30
In $$\triangle ABC, \angle A = 52^\circ$$ 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 $$\angle OBC$$ and $$\angle OCB$$ meetat P, then the measure of $$\angle BPC$$ is:
Solution
By the orthogonal property,
$$\angle BOC = 180 - \angle A$$
$$\angle OBC + $$\angle OCB = \angle A$$
$$\angle BPC = 180 - \angle A/2
$$\angle BPC = 180 - \angle 52/2 = 180 - 26 = 154 \degree$$
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