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Ex 10.4, 4 - If a line intersects two concentric circles - Ex 10.4

Ex 10.4, 4 - Chapter 10 Class 9 Circles - Part 2

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Ex 10.4, 4 If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see figure). Given: Two concentric circles with centre O. & a line intersects the circles at A,B,C & D To prove: AB = CD Proof: Let two circles be C1 & C2 and line be l We draw OP perpendicular to line l In circle C1, OP ⊥ BC So, OP bisects BC, i.e. BP = CP (As OP is perpendicular to line l ) (Perpendicular drawn from centre of a circle to a chord bisects the chord) In circle C2, OP ⊥ AD So, OP bisects AD, i.e. AP = DP (As OP is perpendicular to line l ) (Perpendicular drawn from centre of a circle to a chord bisects the chord) Subtracting (2) & (1), (2) – (1) AP – BP = DP – CP ⇒ AB = CD Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.