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Ex 10.2, 10 - Prove that angle between two tangents drawn - Theorem 10.1: Tangent perpendicular to radius (proof type)

  1. Chapter 10 Class 10 Circles
  2. Serial order wise
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Ex 10.2,10 Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre. Given: A circle with center O. Tangents PA and PB drawn from external point P To prove: ∠ APB + ∠ AOB = 180° Proof: In quadrilateral OAPB ∠ OAP + ∠ APB + ∠ OBP + ∠ AOB = 360° Putting values of angles 90° + ∠ APB + 90° + ∠ AOB = 360° 180° + ∠ APB + ∠ AOB = 360° ∠ APB + ∠ AOB = 360° – 180° ∠ APB + ∠ AOB = 180° Hence proved

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