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In the above figure, PT and RS are 2 parallel lines which are tangents to the circle with centre O. PQ is also a tangent to the circle 
∠ PSO = 30º and PT = 6 units. What is the value of the area of PTOQ?
  • a)
    18√2 ​sq units
  • b)
    18√3 sq units
  • c)
    36 sq units
  • d)
    6√2 sq units
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In the above figure, PT and RS are 2 parallel lines which are tangents...
Let the diameter of the circle be 2r
△SPT is a right-angle triangle.
tan(30º) = 6/2r
1/√3 = 3/r
or r = 3√3. Since PT and PQ are the tangents from same point P, PT = PQ
Area PTOQ = Area PTO + Area PQO

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In the above figure, PT and RS are 2 parallel lines which are tangents to the circle with centre O. PQ is also a tangent to the circle∠ PSO = 30º and PT = 6 units. What is the value of the area of PTOQ?a)18√2 sq unitsb)18√3sq unitsc)36 sq unitsd)6√2sq unitsCorrect answer is option 'B'. Can you explain this answer?
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