For questions about general quadrilaterals (including parallelograms, trapezoids, rhombi) and their properties.

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I have a quadrilateral ABCD. If I know the angles $DAB, DCB, ADB, CDB, ABD, CBD$, can I obtain the angle $DAC$? I know that I can do it by some coordinate geometry or the sine formula, but is there a ...
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### Which quadrilaterals are possible as the intersection of a plane and a rectangular pyramid?

Suppose I have a pyramid with a rectangular base, and consider a plane that does not intersect the base or the apex (it only intersects the four faces incident to the apex). When the plane is parallel ...
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Let $ABCD$ be a cyclic quadrilateral inscribed in a circle of center $O$ and let $AB\cap DC=\{E\}$, $AD\cap BC=\{F\}$ and $AC\cap BD=\{X\}$. Let $OE\cap FX=\{G\}$ and prove that quadrilaterals $AOGB$ ...
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### Circumcenter of acute-$\Delta ABC$ is $O$. Line $AC$ intersects circumcircle of $\Delta AOB$ at point $X$, in addition to vertex $A$. Prove $XO⟂BC$.

PROBLEM The circumcenter of an acute-$\mathtt{\Delta ABC}$ is $\mathtt{O}$. Line $\mathtt{AC}$ intersects the circumcircle of the $\mathtt{\Delta AOB}$ at a point $\mathtt{X}$, in addition to the ...
• 107
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### What is the formula to find the quadrilateral inner quadrilateral side length?

Sorry if it is a silly question. I want to find an inner quadrilateral area for that I need one of the inner quadrilateral lengths. I don't know the formula if you can please help me. Lengths of the ...
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1 vote
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### Given rectangle $ABCD$ with $K$ the midpoint $AD$ and $AD/AB=\sqrt{2}$, find the angle between $BK$ and diagonal $AC$.

Could someone help me with this little problem of geometry of quadrilaterals? In rectangle $ABCD$, let $K$ be the midpoint of side $AD$. If we know that $AD/AB =\sqrt{2}$, find the angle between $BK$ ...
1 vote
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### Tangential Equidiagonal (Irregular) Quadrilateral with integer coordinates

Playing with mathematics this week-end, I ended up with this question I couldn't solve, so I'm asking here. I try to find a Quadrilateral ABCD with integers (cartesian) coordinates (points are on a ...
• 9,970
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### Angles of two connected convex quadrilaterals, all lengths given

Consider two convex quadrilaterals sharing one edge with lines meeting at the endpoints of this edge being collinear, so that the seven edges form another, larger convex quadrilateral (see picture). ...
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### How to construct the centroid of a quadrilateral

I know how to construct the centroid of a quadrilateral as mentioned here. But my question is different from that. We know that if points B,C,G are given in geometry plane and for locating point A ...
1 vote
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1 vote
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### Do the rectangles that circumscribe and share edges with a rhombus have identical dimensions?

I am going to make an app for wrapping presents but I don’t know a lot about useful properties of rhombi and associated rectangles. Given the known dimensions necessary to create a rhombus that ...
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