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# Square inscribed inside a circle question?

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Director
Joined: 29 Nov 2012
Posts: 868

Kudos [?]: 1409 [0], given: 543

Square inscribed inside a circle question? [#permalink]

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18 Jan 2013, 04:16
If the square is inscribed inside a circle, the diagonal of the square will be diameter of the circle? any exceptions to this?
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Kudos [?]: 1409 [0], given: 543

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128604 [1], given: 12180

Re: Square inscribed inside a circle question? [#permalink]

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18 Jan 2013, 04:22
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Expert's post
fozzzy wrote:
If the square is inscribed inside a circle, the diagonal of the square will be diameter of the circle? any exceptions to this?

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

Hence, not only the diagonal of an inscribed square but also the diagonal of an inscribed rectangle will be the diameter of the circle, since rectangle (as well as square) is made of two tight triangles (hypotenuse of right triangle = diagonal).

Hope it's clear.
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Kudos [?]: 128604 [1], given: 12180

Re: Square inscribed inside a circle question?   [#permalink] 18 Jan 2013, 04:22
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