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Find the number of pairs of parallel dia...

Find the number of pairs of parallel diagonals in a regular polygon of 10 sides.

A

`45`

B

`56`

C

`22`

D

`64`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)`
Fix a vertex `A`.
There are `4` parallel diagonals.
There are `5` such sets since the vertices of the `10`-gon can be paired into `5` sets. In each set there are `"^(4)C_(2)` pairs, i.e, a total of `"^(4)C_(2)xx5=30` pairs of diagonals.
Now fix a side `AB`. There are `3` parallel diagonals and `5` such sets.
So, total pairs `=^(3)C_(2)xx5=15`
Hence, net total `=30+15=45`
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