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Shanaya Chopra
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Asked: 2020-10-30T03:36:25+00:00 In:

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.

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NCERT Solutions for Class 10 Maths Chapter 10
Important NCERT Questions
Circles
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 10.2
Page No:214
Questions No:10

2020-2021cbsechapter 10circlesclass10mathematicsncert
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    1. Get Hindi Medium and English Medium NCERT Solution for Class 10 Maths to download.
      Please follow the link to visit website for first and second term exams solutions.
      https://www.tiwariacademy.com/ncert-solutions/class-10/maths/chapter-10/

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      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.

      Let PA and PB are two tangents of circle with centre O. Join OA and OB.
      We know that the radius is perpendicular to tangent. therefore
      ∠OAP = 90° and ∠OBP = 90°.
      In quadrilateral OAPB, ∠OPA + ∠PBO + ∠BOA = 360°
      90° + ∠APB + 90° + ∠BOA = 360° ∠APB + ∠BOA = 180°
      Hence, it is proved 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.

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