If ABCD is a square then show that the sides A,B,C,and D are concyclic

If ABCD is a square then show that the sides A,B,C,and  D are concyclic


1 Answers

Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

First of all, let me tell you what are concyclic points.
The points which lie on the same circle are called concyclic points.
So in this question, it's clear by now that we have to prove that the four vertices of the square are lying on the same circle.

For better understanding, you can refer the image. Now, the condition to prove this is If (AC)(BD) = (AB)(CD) + (BC)(AD).
Here AC = BD = diagonal of the square which is nothing but x root 2.
(x root 2)(x root 2) = 2 x square = L.H.S
R.H.S = (x)(x) + (x)(x) = x square + x square = 2 x square = L.H.S [Hence Proved]

Thanks and Regards

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