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705-805 (Hard)|   Geometry|      
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14101992
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 19 Apr 2017, 08:09
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C
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Difficulty:

75% (hard)

Question Stats:

46% (01:57) correct 54% (01:28) wrong based on 81 sessions

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G is the centre of a regular hexagon ABCDEF. How many triangles can be formed by using vertices from amongst these seven points?

A. 20
B. 25
C. 32
D. 35
E. 38
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C
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 19 Apr 2017, 08:30
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G is the centre of a regular hexagon ABCDEF. How many triangles can be formed by using vertices from amongst these seven points?

A. 20
B. 25
C. 32
D. 35
E. 38
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From 6 points A, B, C, D, E, F, we could form 6C3=20 triangles.

From G, we could choose 2 remain points from 6 points A, B, C, D, E, F to form a triangle. Hence, we could form 6C2=15 triangles.

The total number of triangles we could form is 35.

What did I miss here?
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VyshakhR1995
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 19 Apr 2017, 08:46
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In a regular hexagon three diagonals pass through the centre.
Total number of points 7
Triangle----> 3 at a time ----> 7c3 = 35
But Since three diagonals pass through the centre, G will be collinear in three cases... So 35-3=32
Hope it helps...
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 20 Apr 2017, 08:06
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Okei, the point I did miss here is the definion of regular hexagon. Regular hexagon is when all angles are equal and all sides are equal.
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 20 Apr 2017, 08:44
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14101992
G is the centre of a regular hexagon ABCDEF. How many triangles can be formed by using vertices from amongst these seven points?

A. 20
B. 25
C. 32
D. 35
E. 38
Show more

Hi...

there are 7 points and we have to choose three to form a triangle...
So 7C3=\(\frac{7!}{4!3!}\)=7*5=35..

But the DIAGONAL too is made from 3 points : 2vertices and 1 centre..
And here we make a line and not a triangle..

There are 3 diagonals, so 3 triangles counted in 35 are actually a LINE..

Total left 35-3=32

C
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 21 Jun 2019, 09:15
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G is the centre of a regular hexagon ABCDEF. How many triangles can be formed by using vertices from amongst these seven points?

A. 20
B. 25
C. 32
D. 35
E. 38
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total points - 7 and for ∆ ; 7c3 ; 35
we have 3 diagonal within the figure so total possible ∆ ; 35-3 ; 32
IMO C
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G is the centre of a regular hexagon ABCDEF. How many triangles can be 30 Jul 2025, 04:02
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