Question

If ap and pb are tangents and apb is 40 degree find aqb

Answer 1

Step-by-step explanation:

Join OB.

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

∴  ∠OBP=∠OAP=90o

Now, In a quadrilateral AOBP

⇒  ∠AOB+∠OBP+∠APB+∠OAP=360o               [ Sum of four angles of a quadrilateral is 360o. ]

⇒  ∠AOB+90o+40o+90o=360o

⇒  220o+∠AOB=360o

⇒  ∠AOB=140o.

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

⇒  ∠AOB+∠OAB+∠OBA=180o

⇒  140o+2∠OAB=180o                [ Since, ∠OAB=∠OBA ]

⇒  2∠OAB=40o

∴  ∠OAB=20o