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## virtus 3 years ago 6 POINTS (A,B,C,D,E,F) LIE ON A CIRCLE

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1. SmoothMath

That's cool. Also, nice caps.

2. virtus

|dw:1342406130806:dw|

3. virtus

Find the maximum no. of Points of Intersection of chords inside the circle? LOL @SmoothMath !

4. ramya25

fe || ad || bc ?

5. virtus

huh?

6. SmoothMath

Virtus, why not draw in all of the possible chords?

7. virtus

|dw:1342406517682:dw|

8. sabeelio

oh then just count it

9. SmoothMath

Truedat, sab.

10. virtus

no but you are supposed to use combinations to solve it, Like in the exam you can't just say refer to the diagram. You actually have to show them how you can get the answer through combinations!

11. UnkleRhaukus

well for example (a) can join with 5 other point to make a cord,

12. SmoothMath

Is there any statement about where the points are on the circle?

13. virtus

no there isn't but the answer is 6C4 in case you were wondering

14. UnkleRhaukus

i got \[^6C_2\]

15. UnkleRhaukus

\[^6C_2=15=^6C_4\]

16. virtus

@UnkleRhaukus but then there was a question prior to that that asked How many chords can be drawn by joining these different pairs of points and the answer was 6C2 Why couldn't they have written 6C2 for the second question?

17. UnkleRhaukus

hmm im not sure

18. virtus

do you know where the 4 may have come from then in 6C4?

19. virtus

because i think i understand if it is 2, cause its kinda like that hand shake question then

20. ramya25

ncr = nc(n-r)

21. UnkleRhaukus

is suppose the question is asking the number of intersections the cords make

22. virtus

huh?

23. ramya25

i guess we should calculate # intersections per one point, and multiply it with 6 then we are using counting... not combintions lol

24. SmoothMath

I honestly don't see how it's a combination question, but hey.

25. ramya25

im seeing a pattern maybe we can work backward # intersecting points for point "a" inside the circle : 1.3 + 2.2 + 3.1 = 10 total # of intersecting points possible = 10*6 = 60

26. ramya25

thats the answer. lets see if the pattern means something in combination terms 1.3 + 2.2 + 3.1 r(n) + (r+1)(n-1) + (r+2)(n-2) + ....

27. ramya25

thats same as SUM (r)(n-r)

28. ramya25

|dw:1342408544273:dw|

29. ramya25

this looks more compact than any combination formula... but it would be good to see if this can be converted to NCR s...

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