web analytics

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
Ask Download

Transcript

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

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail