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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


Ex 10.6, 5 (Optional) 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

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.