Question

maths question no 4...need solution urgently

Answer 1

Since the line joining the centre to the external point from which the pair of tangents bisects the angle made by the two tangents. So,

angle OPQ = 1/2 of angle QPR

=60
Since radius is perpendicular to the tangent. So,

angle OQP =90

So by angle sum property of triangle,

angleQOP= 30

Use trigonometric ratio as-

sin angle QOP=pq/op
1/2 = pq/op
op=2pq