P3

Part of 2014 Iranian Geometry Olympiad (junior)

Problems(1)

constant ratio in 2 inscribed 93-gons with parallel sides

Source: IGO 2014 Junior 3

Each of Mahdi and Morteza has drawn an inscribed

93

-gon. Denote the first one by

A_1A_2…A_{93}

and the second by

B_1B_2…B_{93}

. It is known that

A_iA_{i+1} // B_iB_{i+1}

1 \le i \le 93

A_{93} = A_1, B_{93} = B_1

\frac{A_iA_{i+1} }{ B_iB_{i+1}}

is a constant number independent of

i

.
by Morteza Saghafian

ratiogeometrypolygonparallel