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

Question

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).

Shiv2016 · Answer

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.

Bunuel · Answer

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.

Shiv2016 · Answer

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

Mehemmed · Answer

Hi  Bunuel ,

Could please help me with this question.

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?

Leo8 · Answer

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.

coolnaren · Answer

Hi  Bunuel ,

very good question. thanks

Pastillita · Answer

Could someone please tell me if my logic for Statement (1) being insufficient is correct:

(1) the triangle could be right angled, but it also may not be. For example, we could have a triangle with length of 3 units and its an equilateral triangle with all sides equal to 3 units (which is isosceles), this is NOT a RAT. But on the other hand, we could have an isosceles right angled triangle (a 45-45-90 RAT) where the side lengths are 3 units and the other length (hyp) is 3root(2) units long.

Since we are unsure of which we have, (1) is INSUFFICIENT.

(2) tells us that the circle has a circumference of 3pi. This means that the diameter is 3 units. We are told in the q that the triangle that is inscribed in the circle has one side equal to three units. There is a property that states that if you have a triangle inscribed in a circle, and one of its sides is equal to the diameter of that circle, then the triangle has to be a RAT. Hence, (2) alone is sufficient to answer this question because (2) automatically tells us that the inscribed triangle is a RAT as one of its sides = diameter of circle.

Answer is B

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

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

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