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# If a triangle is inscribed in a circle such that a length of a side of

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Intern
Joined: 18 Apr 2013
Posts: 33
If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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06 Jul 2017, 08:06
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Difficulty:

35% (medium)

Question Stats:

67% (01:24) correct 33% (01:20) wrong based on 124 sessions

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If a triangle is inscribed in a circle such that a length of a side of the triangle is 3, is the triangle a right triangle?
1) The triangle is isosceles.
2) The circumference of the circle is 3 (pie).
Director
Joined: 02 Sep 2016
Posts: 649
Re: If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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06 Jul 2017, 12:11
Hello Bunuel

Please explain why option B is correct?

From option B, I found diameter= 3 which can be one side of the triangle but we are already given that one side is equal to 3.

It can be the same side.
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Re: If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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06 Jul 2017, 12:17
Shiv2016 wrote:
Hello Bunuel

Please explain why option B is correct?

From option B, I found diameter= 3 which can be one side of the triangle but we are already given that one side is equal to 3.

It can be the same side.

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 and diameter is hypotenuse.
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Re: If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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07 Jul 2017, 06:11
I solved this question again to understand the concept better.

Method:
One side = 3

We just know that one side of this triangle is 3 and it can be any side.

1) Two sides are equal and thus any two sides of this triangle can be equal but which two sides ?

Not sufficient to conclude anything.

BCE

2) 2*pi*r= 3*pi
r= 1.5

Diameter= 3

We already one side of the triangle is 3 and according to second statement diameter is 3. As we know diameter is the longest side of the triangle and thus no other side will equal 3. We can conclude that it is a right angled triangle.

B
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Re: If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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04 Jan 2018, 12:33
Hi Bunuel,

Stmnt 1 is insufficient

From stmnt 2 we can find the diameter of the circle. But who said that one side of the triangle is on the diameter?
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Re: If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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04 Jan 2018, 13:10
Mehemmed wrote:
Hi Bunuel,

Stmnt 1 is insufficient

From stmnt 2 we can find the diameter of the circle. But who said that one side of the triangle is on the diameter?

you can't have a side of 3 cm of an inscribed triangle that does not coincide with the diameter of the circle, which is also 3 cm.

The longest side an inscribed triangle can have is the diameter of the circle.

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Intern
Joined: 11 Apr 2014
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If a triangle is inscribed in a circle such that a length of a side of  [#permalink]

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04 Jan 2018, 23:38
[quote="Leo8"][quote="Mehemmed"]Hi Bunuel,

very good question. thanks
If a triangle is inscribed in a circle such that a length of a side of   [#permalink] 04 Jan 2018, 23:38
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