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If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80o, ∠POA is
  • a)
    70
  • b)
    40
  • c)
    90
  • d)
    50
Correct answer is option 'D'. Can you explain this answer?
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If tangents PA and PB from a point P to a circle with centre O are inc...
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If tangents PA and PB from a point P to a circle with centre O are inc...
Option D is correct let's see how-->since the tangents drawn from an external point to a circle make 90 degree at the point of contact.we can say that-->angle PAO= angle PBO=90 degree each.Angle APB=80( given)angle sum property we can say that-->angle AOB=100 degreeor, angle POA=100/2=50 degree.
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Community Answer
If tangents PA and PB from a point P to a circle with centre O are inc...
As we know angle PAO = angle PBO = 90 degree
Angle APB = 80 degree ( Given )
Angle APB + Angle PBO + Angle BOA + Angle OAB = 360 degree
80 + 90+Angle BOA + 90 = 360
Angle BOA +260 = 360
Angle BOA = 360 - 260 = 100 Degree

So, angle POA = 100/ 2 = 50 Degree
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If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of80o,∠POAisa)70∘b)40∘c)90∘d)50∘Correct answer is option 'D'. Can you explain this answer?
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