In a circle with centre O, AB is a chord, and AP is a tangent

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In a circle with centre O, AB is a chord, and AP is a tangent to the circle. If ∠AOB = 140°, then the measure of ∠PAB is

1. 35°
2. 55°
3. 70°
4. 75°

Correct Option: C

According to question , we draw a figure of a circle with centre O ,

In ∆ OAB,
Here , OA = OB = radius
∴ ∠OAB = ∠OBA
∴ ∠OAB + ∠OBA + ∠AOB = 180°
∴ 2∠OAB = 180° – 140° = 40°

⇒ ∠OAB =	40	= 20°
	2

∴ ∠PAO = 90°
∴ ∠PAB = 90° – 20° = 70°