Question

Two tangents pl and pm are drawn to a circle with centre o from an external point p.Prove that lpm= 2olm

Answer 1

Answer:MARK IT BEST

Step-by-step explanation:

Answer 2

Tangents are Perpendicular to Radius at Circumference

Step-by-step explanation:

In quadrilateral OLMP,

$\angle$OLP = $\angle$ OMP = 90° (Radius is perpendicular to tangent)

$\angle$LPM + $\angle$OLM + $\angle$PMO + \angle MOL = 360 °

$\angle$LPM + 90° + 90° + $\angle$LOM = 360 °

$\angle$LPM + $\angle$LOM = 180 °

$\angle$LOM = 180° - $\angle$ LPM """(1)

In LOM,  

$\angle$LOM + $\angle$LMO + $\angle$MLO = 180 °

180 - $\angle$LOM + $\angle$LMO + $\angle$MLO = 180° (Using (1))

$\angle$LMO + $\angle$MLO = 180° - 180° + $\angle$LPM

So, 2 $\angle$OLM = $\angle$LPM (As $\angle$LMO = $\angle$MLO, OL = OM) Proved!