Math, asked by rajenderreddy85, 1 month ago

PA and PB are tangents drawn from a point p to the circle with center O if angle APB equal to 60 than what is angle AOB​

Answers

Answered by 24025
1

Answer:

We know that the radius and tangent are perpendicular at their point of contact.

∴ ∠OBP=∠OAP=90

o

Now, In a quadrilateral AOBP

⇒ ∠AOB+∠OBP+∠APB+∠OAP=360

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[ Sum of four angles of a quadrilateral is 360

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. ]

⇒ ∠AOB+90

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+60

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+90

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=360

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⇒ 240

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+∠AOB=360

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⇒ ∠AOB=120

o

.

Since OA and OB are the radius of a circle then, △AOB is an isosceles triangle.

⇒ ∠AOB+∠OAB+∠OBA=180

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⇒ 120

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+2∠OAB=180

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[ Since, ∠OAB=∠OBA ]

⇒ 2∠OAB=60

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∴ ∠OAB=30

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Step-by-step explanation:

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