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computational with a square, collinear given (2011 NZOMC Camp Sel. J5)

Source:

January 3, 2021

squaregeometrydiastancecollinear

Problem Statement

Let a square

ABCD

with sides of length

C

be given. A point

AB

on

BC

is at distance

d

from

C

, and a point

Y

on

CD

is at distance

d

from

C

. The extensions of:

AB

and

DX

meet at

P

,

AD

and

BY

meet at

Q, AX

and

DC

meet at

R

, and

AY

and

BC

meet at

S

. If points

P, Q, R

and

S

are collinear, determine

d

.

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