**MATHMAA**

# 17thKVS-JMO2014-Solutions6

## 17thKVS-JMO2014-Solutions6

## Probability Introduction :

This page has question and solution of 17thKVS-JMO2014-Solutions6 in detail. Before starting this solution we have to know about "Ptolemy's Theorem".

Ptolemy's Theorem :

In Euclidean geometry, **Ptolemy's theorem** is a relation between the four sides and two diagonals of a cyclic quadrilateral . The theorem is named after the Greek astronomer and mathematician Ptolemy.

If the quadrilateral is given with its four vertices *A*, *B*, *C*, and *D* in order, then the theorem states that:

|AC|.|BD|= |AB|.|CD| + |BC|.|AD|.

This relation may be verbally expressed as follows:

*"If a quadrilateral is inscribable in a circle then the product of
the measures of its diagonals is equal to the sum of the products of
the measures of the pairs of opposite sides".*

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6 Q : Suppose
\(A_{1}A_{2}A_{3}........A_{n}\) is an n-sided regular polygon such that
\(\frac{1}{A_{1}A_{2}}\) = \(\frac{1}{A_{1}A_{3}}\) +
\(\frac{1}{A_{1}A_{4}}\) . Determine the number of sides of the polygon

Solution :

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