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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
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
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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
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Hello friend...Hope this helps you...