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Example 5 - Two circles intersect at two points A and B - Angle subtended by arc at the centre

  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Example 5 Two circles intersect at two points A and B. AD and AC are diameters to the two circles (see fig.). Prove that B lies on the line segment DC. Given: Let two circles be C1 & C2. AD is the diameter of circle C1 & AC is the diameter of circle C2 To prove: B lies on CD. Construction: Join AB Proof Now, ∠ ABD + ∠ ABC = 90° + 90° = 180° Since the sum of angles is 180° , they form a linear pair. Linear pair can only happen on a line. Therefore, DBC is a line. ⇒ B lies on the line segment DC. Hence proved

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Davneet Singh
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.
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