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Senior Manager  P
Joined: 15 Feb 2018
Posts: 391
A triangle is inscribed in a circle. The length of one of its sides is  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 56% (01:25) correct 44% (01:25) wrong based on 59 sessions

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A triangle is inscribed in a circle. The length of one of its sides is 3. Is the triangle a right triangle?

1) The triangle is isosceles.
2) The circumference of the circle is 3π.
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Re: A triangle is inscribed in a circle. The length of one of its sides is  [#permalink]

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philipssonicare wrote:
chetan2u wrote:
A triangle is inscribed in a circle. The length of one of its sides is 3. Is the triangle a right triangle?

1) The triangle is isosceles.
It is possible that other sides are 6 and 7...NO
Possible that aides are 4 and 5...yes

chetan2u
If the triangle is isosceles, then can't have sides of 6 and 7, 4 and 5 if one side is 3? Please clarify.
I agree with your explanation for Statement 2.

philipssonicare

Using first statement alone i.e. one side of length 3 and triangle being isosceles triangle

Case 1: If one side is 3 then other sides may be 3 and 4 i.e. Triangle is an isosceles triangle but it's NOT a right triangle. Answer to question is NO

Case 2: If one side is $$3$$ then other sides may be $$3$$ and $$3√2$$ with $$3√2$$ being hypotenuse and diameter of triangle i.e. Triangle is an isosceles triangle and also a right triangle. Answer to question is YES

hence NOT SUFFICIENT
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Re: A triangle is inscribed in a circle. The length of one of its sides is  [#permalink]

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A triangle is inscribed in a circle. The length of one of its sides is 3. Is the triangle a right triangle?

1) The triangle is isosceles.
It is possible that other sides are 6 and 7...NO
Possible that aides are 4 and 5...yes
Insufficient

2) The circumference of the circle is 3π.
$$3\pi=2πr......2r=diameter=3$$..
now the largest possible side of a triangle is diameter and here the side and diameter are equal and 3
So one of the sides of the triangle is the diameter and other two sides are smaller than it.
Any triangle, which has the side as the DIAMETER , is always a right angled triangle as the angle opposite to diameter is 90°
Sufficient

B
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A triangle is inscribed in a circle. The length of one of its sides is  [#permalink]

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chetan2u wrote:
A triangle is inscribed in a circle. The length of one of its sides is 3. Is the triangle a right triangle?

1) The triangle is isosceles.
It is possible that other sides are 6 and 7...NO
Possible that aides are 4 and 5...yes

chetan2u
If the triangle is isosceles, then can't have sides of 6 and 7, 4 and 5 if one side is 3? Please clarify.
I agree with your explanation for Statement 2.
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Re: A triangle is inscribed in a circle. The length of one of its sides is  [#permalink]

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chetan2u wrote:
A triangle is inscribed in a circle. The length of one of its sides is 3. Is the triangle a right triangle?

1) The triangle is isosceles.
It is possible that other sides are 6 and 7...NO
Possible that aides are 4 and 5...yes
Insufficient

2) The circumference of the circle is 3π.
$$3\pi=2πr......2r=diameter=3$$..
now the largest possible side of a triangle is diameter and here the side and diameter are equal and 3
So one of the sides of the triangle is the diameter and other two sides are smaller than it.
Any triangle, which has the side as the DIAMETER , is always a right angled triangle as the angle opposite to diameter is 90°
Sufficient

B

chetan

If triangle is isosceles with one side given of length 3 then other two sides can NOT be 4 and 5 OR 6 and & as highlighted in your explanation of first statement.
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Re: A triangle is inscribed in a circle. The length of one of its sides is  [#permalink]

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Statement 1:
Only tells us two sides have the same length, could be 3 could also be the unknown side - Not Sufficient

For statement 2:
C = 3π thus Diameter = 3
If one of the sides of an inscribed triangle is the diameter of the circle, then the triangle must be a right triangle. - Sufficient

Thus B Re: A triangle is inscribed in a circle. The length of one of its sides is   [#permalink] 22 Oct 2019, 08:20
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