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# Of the 8 points in a given plane 4 are on circle O -Geometry - PS

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Senior Manager
Joined: 08 Jun 2013
Posts: 469
Location: India
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Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

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24 Aug 2018, 19:00
2
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:46) correct 53% (01:55) wrong based on 34 sessions

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Of the 8 points in a given plane 4 are on circle O and remaining 4 are on line L. Number of different quadrilaterals that can be formed by these 8 points are

A) 52

B) 53

C) 54

D) 64

E) 74

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Re: Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

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24 Aug 2018, 20:02
4C3*4C1 + 4C4 + 4C2*4C2 = 53

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Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

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24 Aug 2018, 23:29
Attachment:
Line_Circle.png

We are given a line and circle each which contain 4 points. The 8 points can be the vertices of a quadrilateral.
A line which has 4 collinear points can have a maximum of 2 points which can be the vertices. There are 3 ways
in which a quadrilateral can be formed

1. All 4 vertices are on the circle - $$C_4^4 = 1$$
2. Three vertices are on the circle and one vertice if on the line - $$C_3^4*C_1^4 = 4*4 = 16$$
3. Two vertices are on the circle and two vertices are on the line - $$C_2^4*C_2^4 = 6*6 = 36$$

Therefore, the total number of quadrilaterals that can be formed by these points are 1+16+36 = 53(Option B)
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Re: Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

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25 Aug 2018, 00:30
1
Out of the four points given, A quadrilateral can be formed by selecting $$4$$ points from the $$8$$ points except when:
i) $$4$$ points have been taken from the line
ii) $$3$$ points have been taken from the line and one from circle.

Total required cases $$= 8C4- (4C4+4C3*4C1) = 53$$

Harshgmat wrote:
Of the 8 points in a given plane 4 are on circle O and remaining 4 are on line L. Number of different quadrilaterals that can be formed by these 8 points are

A) 52

B) 53

C) 54

D) 64

E) 74

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Posts: 2099
Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

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25 Aug 2018, 08:57
2
pushpitkc wrote:

Therefore, the total number of quadrilaterals that can be formed by these points are 1+16+36 = 52(Option B)

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Posts: 3307
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Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

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25 Aug 2018, 09:07
generis wrote:
pushpitkc wrote:

Therefore, the total number of quadrilaterals that can be formed by these points are 1+16+36 = 52(Option B)

Thanks for notifying, made the necessary change!
Of the 8 points in a given plane 4 are on circle O -Geometry - PS &nbs [#permalink] 25 Aug 2018, 09:07
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