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Ex 10.2, 5 - Prove that perpendicular at point of contact - Ex 10.2

  1. Chapter 10 Class 10 Circles
  2. Serial order wise
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Ex 10.2,5 Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. Given: Let us assume a circle with centre O & AB be the tangent intersecting circle at point P To prove: OP ⊥ AB Proof: We know that Tangent of circle is perpendicular to radius at point of contact Hence, OP ⊥ AB So, ∠ OPB = 90° Now lets assume some point X , such that XP ⊥ AB Hence, ∠ XPB = 90° From (1) and (2) ∠OPB = ∠ XPB = 90° Which is possible only if line XP passes through O Hence , perpendicular to tangent passes through centre

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.