MathDB

2015 Geometry #5

Source:

December 23, 2016

Problem Statement

Let

I

be the set of points

(x,y)

in the Cartesian plane such that

x>\left(\frac{y^4}{9}+2015\right)^{1/4}

Let

f(r)

denote the area of the intersection of

I

and the disk

x^2+y^2\le r^2

of radius

r>0

centered at the origin

(0,0)

. Determine the minimum possible real number

L

such that

f(r)<Lr^2

for all

r>0

.

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