Question

if from external point P of a circle with center O , two tangent PQ and PR are drawn such that angle opr is 120 prove 2pq=po

Answer 1

In ▲OPQ, we have

∠PQO=90⁰ (the tangent at any point is perpendicular to the radius through the point of contact) and
∠QPO=1/2 X ∠QPR= 1/2 X 120⁰= 60⁰ (the two tangents drawn from an external point are equally inclined to the line segment joining the centre to that point and so ∠QPO=∠RPO)

Now, In right ▲OPQ, we have cos(∠QPO)=PQ/PO

COS 60⁰ = PQ/PO

1/2=PQ/PO

2PQ=PO

HENCE PROVED


hope this helps you

Answer 2

PO bisects angleQPR