MathDB

locus

Source: Ireland 1993

June 29, 2009

geometry proposedgeometry

Problem Statement

A line

l

is tangent to a circle

S

at

A

. For any points

B,C

on

l

on opposite sides of

A

, let the other tangents from

B

and

C

to

S

intersect at a point

P

. If

B,C

vary on

l

so that the product

AB \cdot AC

is constant, find the locus of

P

.

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