in the figure ,PQ is a tangent to a circle with Centre O. If angle OAB is equals to 30° find angle ABP and Angle AOB
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Answer:
angle ABP=60,angle AOB=120
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Since AO and OB is radius of circle
Therefore AO = OB
∠OAB = ∠OBA ( angle opp. to equal side)
∠OBA = 30°
NOW,
since radius is perpendicular to tangent
⇒∠ABO +ABP = ∠OBP
⇒ 30° + ∠ABP = 90°
∠ABP = 60°
And
In ΔAOB
∠OAB + ∠ABO + ∠AOB = 180° (ASP)
30 ° + 30 + ∠AOB = 180°
∠AOB = 120°
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