MathDB

Constant point

Source: Iran PPCE 2007

March 23, 2007

geometry proposedgeometry

Problem Statement

Let

(C)

and

(L)

be a circle and a line.

P_{1},\dots,P_{2n+1}

are odd number of points on

(L)

.

A_{1}

is an arbitrary point on

(C)

.

A_{k+1}

is the intersection point of

A_{k}P_{k}

and

(C)

(

1\leq k\leq 2n+1

). Prove that

A_{1}A_{2n+2}

passes through a constant point while

A_{1}

varies on

(C)

.

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