MathDB

2015 Geometry #10

Source:

December 23, 2016

Problem Statement

Let

\mathcal{G}

be the set of all points

(x,y)

in the Cartesian plane such that

0\le y\le 8

and

(x-3)^2+31=(y-4)^2+8\sqrt{y(8-y)}.

There exists a unique line

\ell

of negative slope tangent to

\mathcal{G}

and passing through the point

(0,4)

. Suppose

\ell

is tangent to

\mathcal{G}

at a unique point

P

. Find the coordinates

(\alpha, \beta)

of

P

.

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