tangents PS and PT are drawn to a circle with centre O such that angle(SOT) = 120o,prove that 4(PS2) = - Maths - Circles

Question

tangents PS and PT are drawn to a circle with centre O such that
angle(SOT) = 120o,prove that 4(PS2) =
3(OP2)

Ashwini Kumar · Accepted Answer

Dear Student,

Please find below the solution to the asked query:
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We have,∠SOT=120°⇒∠SOT2=120°2⇒∠SOP=60°Now, in right-angled triangle OSP, we havesin∠SOP=PSOP⇒sin60°=PSOP⇒32=PSOP⇒322=PSOP2⇒34=PS2OP2∴4PS2=3OP2Hence, proved

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tangents PS and PT are drawn to a circle with centre O such that angle(SOT) = 120o,prove that 4(PS2) = 3(OP2)

tangents PS and PT are drawn to a circle with centre O such that angle(SOT) = 120^o,prove that 4(PS²) = 3(OP²)