OA = OB∴ ΔOAB is an isosceles triangle.⇒ ∠OAB = ∠OBA = 35°⇒ ∠AOB = 180° – 2 × 35° = 110°We know that radius from the CENTRE of the CIRCLE to the point of tangency is PERPENDICULAR to the tangent line.∴ In quadrilateral APBO,∠OAP = ∠OBP = 90°⇒ ∠APB = 360° – 2 × 90° – 110° = 70°

"> OA = OB∴ ΔOAB is an isosceles triangle.⇒ ∠OAB = ∠OBA = 35°⇒ ∠AOB = 180° – 2 × 35° = 110°We know that radius from the CENTRE of the CIRCLE to the point of tangency is PERPENDICULAR to the tangent line.∴ In quadrilateral APBO,∠OAP = ∠OBP = 90°⇒ ∠APB = 360° – 2 × 90° – 110° = 70°

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PA and PB are two tangents to a circle with centre O, from a point P outside the circle. A and B are points on the circle. If ∠OAB = 35°, then ∠APB is equal to∶

SRMJEEE Analytical Geometry in SRMJEEE 1 year ago

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Given, ∠ OAB = 35°In ΔOAB,Since OA = OB∴ ΔOAB is an isosceles triangle.⇒ ∠OAB = ∠OBA = 35°⇒ ∠AOB = 180° – 2 × 35° = 110°We know that radius from the CENTRE of the CIRCLE to the point of tangency is PERPENDICULAR to the tangent line.∴ In quadrilateral APBO,∠OAP = ∠OBP = 90°⇒ ∠APB = 360° – 2 × 90° – 110° = 70°

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