query: A problem on Angle bisectors of a triangle and perpendiculars.
positive_passages.docid: 24147
positive_passages.text: $AG,AF$ are perpendiculars to the internal bisectors $CG,BF$ and $GF$ extended intersects $AB,AC$ at $H,I$
negative_passages.docid: 101493
negative_passages.text: Prove that one diagonal of a quadrilateral bisects the other
negative_passages.docid: 92267
negative_passages.text: Adjacency matrix and existence of triangle
negative_passages.docid: 84686
negative_passages.text: Geometric Description Of a Set In The Complex Plane
negative_passages.docid: 22540
negative_passages.text: Bisecting line segments in a tetrahedron.
negative_passages.docid: 111903
negative_passages.text: An inequality for sides of a triangle
negative_passages.docid: 130851
negative_passages.text: Squaring the plane, with consecutive integer squares. And a related arrangement
negative_passages.docid: 37794
negative_passages.text: Proving the two given vectors are orthogonal
negative_passages.docid: 50417
negative_passages.text: Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
negative_passages.docid: 136644
negative_passages.text: Cyclic Quadrilateral Problems
negative_passages.docid: 157213
negative_passages.text: Application of Luca's theorem
negative_passages.docid: 157171
negative_passages.text: Gauss circle problem : a simple asymptotic estimation.
negative_passages.docid: 112896
negative_passages.text: Construct the triangle with given angle bisectors
negative_passages.docid: 62126
negative_passages.text: Constructing a triangle given 2 sides and the inscribed circle's radius
negative_passages.docid: 65372
negative_passages.text: Triangles defined on an infinite Go board by same-colored stones
negative_passages.docid: 63314
negative_passages.text: Triangular Factorials
negative_passages.docid: 28719
negative_passages.text: Question about Angle-Preserving Operators