Question

In the figure PA andPB are tangents.If angle PAB =70degree,what is the measurement of angleACB

Answer 1

Measurement of angle ABC=110 degree

Answer 2

Answer:

Join OB.

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

o

[ Sum of four angles of a quadrilateral is 360

o

. ]

⇒ ∠AOB+90

o

+60

o

+90

o

=360

o

⇒ 240

o

+∠AOB=360

o

⇒ ∠AOB=120

o

.

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

⇒ ∠AOB+∠OAB+∠OBA=180

o

⇒ 120

o

+2∠OAB=180

o

[ Since, ∠OAB=∠OBA ]

⇒ 2∠OAB=60

o

∴ ∠OAB=30

o

Step-by-step explanation:

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