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

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.

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