The rectangle $ABCD$ lies inside a circle. The rays $BA$ and $DA$ meet this circle at points $A_1$ and $A_2$. Let $A_0$ be the midpoint of $A_1A_2$. Points $B_0$, $C_0, D_0$ are defined similarly. Prove that $A_0C_0 = B_0D_0$.
Problem
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Tags: geometry
AlastorMoody
06.03.2019 16:12
Let $\ell_1$ be parallel to $BC$ through $O$ and Let $\ell_2$ be the parallel to $AB$ through $O$, Set $\ell_2$ as $X-$axis and $\ell_1$ as $Y-$axis, and then elegant coord bash
SHREYAS333
06.03.2019 16:14
Same solution
62861
06.03.2019 16:19
Unless I missed something, this is the same problem (but with a different configuration) as Sharygin 2017/2.
Pluto1708
06.03.2019 16:44
Complex bash is also clean
ayan_mathematics_king
27.04.2019 15:10
AlastorMoody wrote: Let $\ell_1$ be parallel to $BC$ through $O$ and Let $\ell_2$ be the parallel to $AB$ through $O$, Set $\ell_2$ as $X-$axis and $\ell_1$ as $Y-$axis, and then elegant coord bash AlastorMoody wrote: Let $\ell_1$ be parallel to $BC$ through $O$ and Let $\ell_2$ be the parallel to $AB$ through $O$, Set $\ell_2$ as $X-$axis and $\ell_1$ as $Y-$axis, and then elegant coord bash $O$ is the centre of rectangle or the circle??