Chapter 10 Class 10 Circles

Serial order wise

Last updated at April 16, 2024 by Teachoo

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