Question

AP and BP are the tangents to a circle of centre ‘O’. If APB = 300 then the measure of OAP is​

Answer 1

Answer:

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Answer 2

Given PA & PB are tangent to the circle with center O.

PA=PB [length of tangent from external point to circle are equal]

In ΔPAB

PA=PB

∠PBA=∠PAB [isosceles triangle]

now ∠PAB+∠PBA+∠APB=180°

[Angle sum prop]

2∠PAB=180−50=130

∠PBA=∠PAB=65 °

Now PA is tangent & OA is radius at point A.

∠OAP=90°

[tangent at any point is ⊥ to radius]

∠OAB=∠OAP−∠PAB=90−65=25°

Hence angle OAB is 25°