MathDB

2011 PUMaC Geometry B4

Source:

September 24, 2019

geometry

Problem Statement

Let

\omega

be a circle of radius

6

with center

O

. Let

AB

be a chord of

\omega

having length

5

. For any real constant

c

, consider the locus

\mathcal{L}(c)

of all points

P

such that

PA^2 - PB^2 = c

. Find the largest value of

c

for which the intersection of

\mathcal{L}(c)

and

\omega

consists of just one point.

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