Question

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Tangent segments PS and PT are drawn to a circle with Centre O such that angle SPT equals to 120 degree. prove that OP =2 PS

Answer 1

HELLO DEAR,


IN ΔOPS AND ΔOPT

OS = OT ( RADIUS)

∠OSP = ∠OTP = 90

(TANGENTS ARE PERPENDICULAR TO THE
RADII)

SP =ST

( TANGENTS TO A CIRCLE FROM THE
EXTERNAL POINT ARE CONGRUENCE)

ΔOPS ≅ ΔOPT  ( By SAS CRITERION)



(THE CORRESPONDING PARTS OF THE
CORRESPONDING TRIANGLES ARE
CONGRUENCE)



<OPS= ∠OPT



SINCE ,



∠SPT = 120° and ∠OPS = ∠OPT



WE HAVE,



∠OPS = ∠OPT = 60°



∠POS = ∠POT = 30°



IN A ΔPOS




sin 30° = PS / OP



1 / 2 = PS / OP



OP = 2PS.


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hello friend...

Hope this helps you...