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प्रश्न
In the figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to ______.
पर्याय
25°
30°
40°
50°
उत्तर
In the figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to 25°.
Explanation:
Given: A circle with center O and PA and PB are tangents to circle from a common external point P to point A and B respectively and ∠APB = 50°
To find: ∠OAB
OA ⊥ AP and OB ⊥ PB ...[As tangent to at any point on the circle is perpendicular to the radius through point of contact]
∠OBP = ∠OAP = 90° ...[1]
In Quadrilateral AOBP ...[By angle sum property of quadrilateral]
∠OBP + ∠OAP + ∠AOB + ∠APB = 360°
90° + 90° + ∠AOB + 50° = 360°
∠AOB = 130° ...[2]
Now in ΔOAB
OA = OB ...[Radii of same circle]
∠OBA = ∠OAB ...[3]
Also, By angle sum property of triangle
∠OBA + ∠OAB + ∠AOB = 180°
∠OAB + ∠OAB + 130° = 180° ...[Using 2 and 3]
2∠OAB = 50°
∠OAB = 25°
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