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Ex 10.6, 5 (Optional) - Prove that circle drawn with any side of rhomb

Ex 10.6, 5 (Optional) - Chapter 10 Class 9 Circles - Part 2

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Question 5 Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonal. Given: Let ABCD be the rhombus and a circle is drawn taking AB as diameter To Prove: Point E lies on the circle Construction: Let point E be intersection of diagonals AC & BD Proof: We know that Diagonals of a rhombus bisect each other at right angles Hence, ∠AEB = 90° Now, AB is the diameter and it subtends right angle at point E. We know that Diameter subtends 90° at any point on circle. So, point E must lie on the circle 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.