Changes

==Algorithm==

==Algorithm==

OP=OQ ----  radii of the same circle

OP=OQ ----  radii of the same circle

OA is joined.

OA is joined.<br>

In quadrillateral APOQ ,

In quadrillateral APOQ ,

∠APO=∠AQO= [radius drawn at the point of contact is perpendicular to the tangent]

∠APO=∠AQO= [radius drawn at the point of contact is perpendicular to the tangent]

  ∠PAQ+∠POQ=  

∠PAQ+∠POQ=  

  Or, ∠PAQ+∠POQ=  

Or, ∠PAQ+∠POQ=  

          ∠PAQ = -∠POQ ----------1

∠PAQ = -∠POQ ----------1

Triangle POQ is isoscles. Therefore ∠OPQ=∠OQP

Triangle POQ is isoscles. Therefore ∠OPQ=∠OQP

∠POQ+∠OPQ+∠OQP=

∠POQ+∠OPQ+∠OQP=

 

Or  ∠POQ+2∠OPQ=

Or  ∠POQ+2∠OPQ=

2∠OPQ=- ∠POQ  ------2

      2∠OPQ=- ∠POQ  ------2

From 1 and 2  

From 1 and 2  

  ∠PAQ=2∠OPQ

∠PAQ=2∠OPQ