Question

in figure, PA and PB are two tangents from an external point P to a circle with centre O if angle PBA=65° find angle OAB

Answer 1

angle PBA= angle PAB=65 degree

angle OAP= 90 degree= angle OAB + angle PAB

                     90 degree= angle OAB + 65 degree

                    angle OAB = 90 - 65 degree

                                       =25 degree

Hope it helps you!!!!!!!!

Answer 2

Answer:

∠ OAB = 25 °

Step-by-step explanation:

Given: Circle with centre O

           ∠PBA = 65°

To find: ∠OAB

Figure Attached

∠PBO = 90° (Because Tangent and radius are perpendicular to each other

                      at point of contact)

⇒ ∠OBA + ∠PBA = 90° (from figure)

⇒ ∠OBA + 65° = 90°

⇒ ∠OBA = 90 - 65

⇒ ∠OBA = 25°

Now, in ΔAOB

AO = OB (radius of same circle)

⇒ ∠OBA = ∠OAB (because Angles opposite to equal sides are equal)

⇒ ∠ OAB = 25 °