Question

In ΔAPQ, AO = OP = OQ. Prove that ∠POQ = 2 × ∠PAQ

Answer 1

Answer:

AO = OP = OQ,

So that the triangle is equilateral triangle.

There also all the angle at the vertices A, P, Q are equal.

PAQ = AQP = QPA = 180/3 = 60

Also, note that as AO = OP = OQ so, this is centroid, incentre, and orthocentre of the triangle.

So the AO, PO, QO bisects the angles

PAQ = AQP = QPA = 60/2 = 30

Now the angle,

POQ = 180 - 30 - 30 = 120

So, it is clearly seen that

∠POQ = 2 × ∠PAQ