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

Ex 10.2, 5 - Chapter 10 Class 10 Circles - Part 2

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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 has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.