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Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?

I. 0.001

II. 0.010

III. 0.100

A. I only B. III only C. II and III only D. I, II, and III E. not I, II, or III

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Hi @kritu there can be many points in a circle none of which are parallel, hence we can construct as small a traingle as possible. However there will be restrictions when asked about the largest perimeter of the triangle.

If it is possible, could you show us the graph/picture? I think the visual graph/picture can help to understand the solution better?

Many thanks!

Bunuel wrote:

Official Solution:

Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?

I. 0.001

II. 0.010

III. 0.100

A. I only B. III only C. II and III only D. I, II, and III E. not I, II, or III

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

I think this is a high-quality question and I agree with explanation. Hi,

What would be the maximum perimeter of ther triangle ? Options given are very small in number, so we can mark all of them. But, if any one option had a large value such as 4 or 5 etc, then how would be solve? Pls help.

Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?

I. 0.001

II. 0.010

III. 0.100

A. I only B. III only C. II and III only D. I, II, and III E. not I, II, or III

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D

Hi,

Why should be place all three vertices on a tiny arc of less than 0.001? I mean how can we find 0.001?

Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?

I. 0.001

II. 0.010

III. 0.100

A. I only B. III only C. II and III only D. I, II, and III E. not I, II, or III

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D

Hi,

Why should be place all three vertices on a tiny arc of less than 0.001? I mean how can we find 0.001?

The solution implies that we can choose three points on a circle so that the area of a triangle will be as small as we want it to be. It does not matter how we can find the area then, important thing is that the minimum are of an inscribed triangle is not limited.

With all due respect, I hope you are not confusing inscribed with circumscribed.

in the wikipedia link : circle is inscribed and polygons are circumscribed

but in our question the case is reversed. the triangle is inscribed in a circle. In general term a triangle inside a circle where all of the vertices of the triangle touches the circle. in such a case try to put these vertices on circumference very very close and then the options given would seem valid.
_________________

Damn it. It makes sense after reading the answer. I assumed third point of triangle will be on opposite side (like outward not inward)
_________________

Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?

I. 0.001

II. 0.010

III. 0.100

A. I only B. III only C. II and III only D. I, II, and III E. not I, II, or III

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D

Dear Bunuel, I'm still hard to understand this explanation. Would you mind to share the picture or maybe link related to the inscribed triangle?