query: Geometry Quadrilateral Proof Question
positive_passages.docid: 157477
positive_passages.text: Area of a quadrilateral proof
negative_passages.docid: 118716
negative_passages.text: If $ABCD$ is a cyclic quadrilateral, then $AC\cdot(AB\cdot BC+CD\cdot DA)=BD\cdot (DA\cdot AB+BC\cdot CD)$
negative_passages.docid: 46106
negative_passages.text: Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
negative_passages.docid: 125702
negative_passages.text: There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
negative_passages.docid: 79777
negative_passages.text: An olympiad Geometry problem involving triangles
negative_passages.docid: 35629
negative_passages.text: Trisect a quadrilateral into a $9$-grid; the middle has $1/9$ the area
negative_passages.docid: 150707
negative_passages.text: Prove the statement 'World is not flat'
negative_passages.docid: 39015
negative_passages.text: Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
negative_passages.docid: 79686
negative_passages.text: How can I prove these statements?
negative_passages.docid: 152311
negative_passages.text: Proving expression$\geq 2$, where variables are $x,y,z$
negative_passages.docid: 156596
negative_passages.text: Prove $r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2$ for a triangle with sides $a$, $b$, $c$, circumradius $R$, inradius $r$, exradii $r_1$, $r_2$, $r_3$
negative_passages.docid: 51120
negative_passages.text: Is this a valid proof for the reverse triangle inequality: Given $x,\,y\in\mathbb{R}^n$, $\|x-y\|\ge |\|x\| - \|y\||$.
negative_passages.docid: 44980
negative_passages.text: Prove that two paths on opposing corners of the unit square must cross.
negative_passages.docid: 82056
negative_passages.text: Quadrilateral problem with midpoints of diagonals
negative_passages.docid: 91662
negative_passages.text: Proof for triangle inequality for vectors
negative_passages.docid: 84334
negative_passages.text: How to prove the Pythagoras theorem using vectors
negative_passages.docid: 50417
negative_passages.text: Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.