MathDB

Square on a Coordinate Plane

Source:

November 13, 2005

analytic geometrytrigonometryquadraticsgeometrygeometric transformationrotationreflection

Problem Statement

Square

ABCD

has center

O

,

AB=900

,

E

and

F

are on

AB

with

AE<BF

and

E

between

A

and

F

,

m\angle EOF =45^\circ

, and

EF=400

. Given that

BF=p+q\sqrt{r}

, wherer

p,q,

and

r

are positive integers and

r

is not divisible by the square of any prime, find

p+q+r

.

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