Ex 10.5, 10 - If circles are drawn taking two sides of - Ex 10.5

  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Ex 10.5, 10 If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side Given: ABC Side AB as diameter for circle C1 & side AC as diameter for C2 Point of intersection of C1 & C2 is A & D To prove: Point of intersection lies in 3rd side, i.e., D lies on BC. Construction: Let us join AD Proof Now, ADB + ADC = 90 + 90 = 180 Since the sum of angles is 180 , they form a linear pair. Linear pair can only happen on a line. Therefore, BDC is a line. D lies on the line segment BC. Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.