If tangents pa and pb from a point p
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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 80°, then ∠POA is equal to(a) 50° (b) 60° (c) 70° (d) 80°
Asked by admin @ in Math viewed by 362 People
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to(a) 50° (b) 60° (c) 70° (d) 80°
Answered by admin @
Given : tangents PA and PB from a point P to a circle with centre O, are inclined to each other at an angle of 80°,
To Find : ∠POA
Solution:
PA & PB are tangent and O is tangent
=> ∠OAP = ∠ OBP = 90°
PA and PB are inclined to each other at 80°
=> ∠APB = 80°
in Quadrilateral OAPB
∠AOB + ∠OAP + ∠APB + ∠ OBP = 360°
=> ∠APB + 90° + 80° + 90° = 360°
=> ∠APB = 100°
∠POA = ∠POB = (1/2) ∠APB
=> ∠POA = (1/2) 100°
=> ∠POA = 50°
option a is correct
Learn More:
in figure line TA is tangent at point T angle TPA=60° and PA= 7.8cm ...
In the figure PA and PB are tangents of a circle with Centre O if angle
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