- #1
Saitama
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Homework Statement
Let A, B, C, D be distinct points on a circle with centre O. If there exists non zero real numbers x and y such that ##|x\vec{OA}+y\vec{OB}|=|x\vec{OB}+y\vec{OC}|=|x\vec{OC}+y\vec{OD}|=|x \vec{OD}+y\vec{OA}|##, then which of the following is always true?
A)ABCD is a trapezium
B)ABCD is a rectangle
C)ABCD is a rhombus
D)ABCD is a square
Homework Equations
The Attempt at a Solution
Honestly, I have no idea how to begin with this problem. Should I start by squaring the moduli? I don't know if that would help.
Any help is appreciated. Thanks!