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MATHMAA

# 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:

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 :