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ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC?

ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC? Correct Answer 120

We, know that the orthocentre is the intersection point of all the altitudes made by the vertices on their corresponding sides

Let take BR and CT as the altitudes

So, in quadrilateral ARPT

∠ATP = ∠ARP = 90°

Since, sum of the opposite angles of quadrilateral = 180°

Hence, it is a cyclic quadrilateral

So, ∠A + ∠BPC = 180°

⇒ ∠BPC = 180° - 60°

∴ ∠BPC = 120°

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