Question

from an external point P tangents PA and PB are drawn to a circle. if angle PAB is 50degree find angle AOB

Answer 1

PA=PB
(Tangents drawn from same external points are
⇒∠PAB=∠PBA
(Angtles opposite to equal sides are equal)
∠PAB=∠PBA=50°
Now,
∠PAO=∠PBO=90°
(Tangents are perpendicular to radius)
∠BAO=∠PAO−∠PAB
=90°−50°=40°
∠ABO=∠PBO−∠PBA
=90°−50°=40°
In △AOB,
∠AOB+∠ABO+∠BAO=180°
(Angle Sum Property)
∠AOB+40°+40°=180°
∠AOB+80°=180°
∠AOB=100° ANS...


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Answer 2

80 degree is angel AOB