Mathematics
In the adjoining figure, PA and PB are tangents to a circle with centre O. If ∠APB = 50°, then ∠OAB is equal to
25°
30°
40°
50°
Answer
In the given figure,
PA and PB are tangents to the circle with centre O.
∠APB = 50°
Since sum of opposite angles of quadrilateral = 180°.
∴ ∠AOB + ∠APB = 180°
⇒ ∠AOB + 50° = 180°
⇒ ∠AOB = 180° - 50° = 130°.
In △OAB,
OA = OB (Radius of the same circle)
Hence, △OAB is an isosceles triangle with ∠OAB = ∠OBA.
Since, sum of angles of a triangle = 180°.
In △OAB,
⇒ ∠OAB + ∠OBA + ∠AOB = 180°
⇒ ∠OAB + ∠OAB + 130° = 180°
⇒ 2∠OAB = 180° - 130°
⇒ 2∠OAB = 50°
⇒ ∠OAB = 25°.
Hence, Option 1 is the correct option.
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