If PA and PB are tangents drawn from an external point P to a circle with centre O such that ∠APB = 70°, then find the value of ∠OAB.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 35°
| Understanding/Application |
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∠APB = 70° PA and PB are tangents to the circle with centre O. ∠OAP = 90°, ∠OBP = 90° |
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In quadrilateral OAPB, ∠AOB + ∠OBP + ∠APB + ∠OAP = 360° ∠AOB + 90 + 90 + 70 = 360 ∠AOB = 110° In triangle OAB, OA = OB In a triangle the angles opposite to equal sides are equal. ∠OBA = ∠OAB In triangle OAB, ∠AOB + ∠OBA + ∠OAB = 180° 110 + 2∠OAB = 180 2∠OAB = 70 ∠OAB = 35° |