MathDB

given double area, find an angle, squares related (May Olympiad 2004 L1)

Source:

May 11, 2019

geometrysqauareareasfind angle

Problem Statement

In a square

ABCD

of diagonals

AC

and

BD

, we call

O

at the center of the square. A square

PQRS

is constructed with sides parallel to those of

ABCD

with

P

in segment

AO, Q

in segment

BO, R

in segment

CO, S

in segment

DO

. If area of

ABCD

equals two times the area of

PQRS

, and

M

is the midpoint of the

AB

side, calculate the measure of the angle

\angle AMP

.

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