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Q01 |
- Diagram : Six points on circle
- Q02 | - Three points on circle making chords
- Q03 | - Four points on circle making chords
- Q04 | - Five points on circle making chords
- Q05 | - Eleven points on circle making chords
- Q02 | - Three points on circle making chords
Q01. Diagram :
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Q02. Three points on circle making chords
Question
- Three points on circle
- How many chords can be drawn ?
- Let 3 points be A, B, C
- Two chords : Chords AB, AC
- One chord : Chord BC
- Total = 1 + 2 = 3
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Q03. Four points on circle making chords
Question
- Four points on circle
- How many chords can be drawn ?
- Let 4 points be A, B, C, D
- Point A : 3 chords AB, AC, AD
- Point B : 2 chords BC, BD
- Point C : 1 Chord CD
- Total = 1 + 2 + 3 = 6
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Q04. Five points on circle making chords
Question
- Five points on circle
- How many chords can be drawn ?
- Let 5 points be A, B, C, D, E
- Point A : 4 chords AB, AC, AD, AE
- Point B : 3 chords BC, BD, BE
- Point C : 2 Chords CD, CE
- Point D : 1 chord DE
- Total = 1 + 2 + 3 + 4 = 10
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Q05. Eleven points on circle making chords
Question 1
- How manu chords can be made if 11 points are on circle ?
- 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 chords
- How manu chords can be made if 101 points are on circle ?
- 1 + 2 + 3 + 4 + .....+ 96 + 97 + 98 + 99 + 100 = 5050 chords
- What is the sequence of number of chords : 3, 6, 10, 15 .... ?
- It is triangular number sequence.
- nth term is T(n) = n*(n + 1)/2
- Sum of n terms S(n) = Sum[n*(n + 1)/2] = n*(n + 1)*(n + 2)/6
- Subject | Prove that Sum[n*(n + 1)/2] = n*(n + 1)*(n + 2)/6
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