ds:geometry13

Question

please explain

FN · Answer

where did you get this question from?

all are possible...

mirhaque · Answer

Can you pls explain your logic baner?

coolcal · Answer

i would like to know the logic as well. i can't think of a circle with a inscribed triangle where any one side of the triangle is less than the radius of the circle

gmat2me2 · Answer

Thats what my reasoning too but I am sure Baner would have owin reason

banerjeea_98 · Answer

ok....let's see if I can explain.....imagine a circle with a very small chord, u can create a triangle using that chord as a base and using a point on the circumference in the circle. None of the sides have to be equal to the radius. u can create as many chords in the circle and create as many triangles out of it. So all of the perimeters are possible. Needless to say this is not a GMAt type question.

yes, if u have a chord (small one) u have 2 points of the triangle on the circumference (right ?) now all u need is to find another point on the circumference to create a triangle...makes sense ?

coolcal · Answer

I can imagine it now!!!! thanks Banerjee a :-D

gmat2me2 · Answer

Inscribe means shouldnt all the triangle vertices lie on the circumference of the circle??
I am asking a trivial query but yes I am in a doubt now.....

kenmore3233 · Answer

I would have thought exactly the same as you, gmat2.

banerjeea_98 · Answer

yes, if u have a chord (small one) u have 2 points of the triangle on the circumference (right ?) now all u need is to find another point on the circumference to create a triangle...makes sense ?

MA · Answer

agree with. that makes sense. actually, i was thinking that way and sure that it should be all because such a wired question normally have that kind of answer too.

gmat2me2 · Answer

OK then coming back to our question if the radius of the circle is 1 how do we deduce that the three values as the perimeters of the different triangle? 

We may take a small chord but the triangle to complete we (may) need longer line segments to complete the triangle . Right? At this point I am not clear. how we can say that all are the valid perimeters.....

ashkg · Answer

I was thinking all 3 are possible. I drew a triangle inscribed in the circle. Now lets reduce the sides of the triangle as much as we can.

btw, what is the OA ?

gmat2me2 · Answer

Agreed with your diagram but not the proof....If we were to be influenced by the figures we draw at least in geometry are bound to make mistakes...Thats the point I wanted to make.....There is no guarantee that the perimeter that you have drawn is less the radius of the circle....If proved yes I agree.... BTW its high time that we have the OA..... :lol:

anirban16 · Answer

All 3 are possible. The triangle can be infinitesimally small. The biggest triangle will be an equilateral triangle of each side = sqrt(3). Hence perimeter (largest possible ) = 3sqrt(3).

There is only an upper limit of perimeter but no lower limit.

The OA is All 3 possible. I took this very problem in one of my tests last week.

ds:geometry13

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