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rectangle out of 2 circles & perpendiculars

Source: Nordic Mathematical Contest 1998 #2

October 3, 2017

geometryrectangle

Problem Statement

Let

C_1

and

C_2

be two circles intersecting at

A

and

B

. Let

S

and

T

be the centres of

C_1

and

C_2

, respectively. Let

P

be a point on the segment

AB

such that

|AP|\ne |BP|

and

P\ne A, P \ne B

. We draw a line perpendicular to

SP

through

P

and denote by

C

and

D

the points at which this line intersects

C_1

. We likewise draw a line perpendicular to

TP

through

P

and denote by

E

and F the points at which this line intersects

C_2

. Show that

C, D, E,

and

F

are the vertices of a rectangle.

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