Question

Please solve question 18 of image

Answer 1

Let angle OLM = x (1)

Then Angle MLP = 90° - x (Tangent is perpendicular to the radius through the point of contact)

Since Tangents drawn from an external point to a circle are equal in length.

This implies that,
PL = PM
Angle PML = Angle PLM = 90°-x (angles opposite to equal sides are equal.)


Now,
angle PLM + angle PML + angle LPM = 180°
90°- x +90°-x +Angle LPM = 180°
Angle LPM = 2x (2)

From (1) and (2),

2Angle OLM = Angle LPM.