Question -
Answer -
Given : From a point P. Out side the circle with centre O, PA and PB are tangerts drawn and тИаAPB = 120┬░
OP is joined To prove : OP = 2 AP
Const: Take mid point M of OP and join AM, join also OA and OB.
┬а
Proof : In right тИЖOAP,
тИаOPA = 1/2 тИаAPB = 1/2 x 120┬░ = 60┬░
тИаAOP = 90┬░ тАУ 60┬░ = 30┬░
M is mid point of hypotenuse OP of тИЖOAP
MO = MA = MP
тИаOAM = тИаAOM = 30┬░ and тИаPAM = 90┬░ тАУ 30┬░ = 60┬░
тИЖAMP is an equilateral triangle
MA = MP = AP
But M is mid point of OP
OP = 2 MP = 2 AP
Hence proved.