- GeometriumA new generalization of Bottema's theoremArea of a rhombusArea of a regular convex pentagonA conic inside a hexagonAn ellipse inside a heptagonIntersecting circlesConcurrent point in an arbitrary triangleA generalization of Droz-Farny line theoremEqual sums of triangle areasA generalization of Thébault's theoremA rhombus inside a parallelogramSquare inside a squareEquilateral triangle inside an equilateral triangleA concyclic points inside a pentagonPoint of concurrency in an arbitrary trianglePoint of concurrency in a cyclic pentagonPoint of concurrency in a cyclic quadrilateralCongruent triangles inside an arbitrary triangleTwo congruent trianglesIntersection point of the perpendicular linesPoint of intersection of the normalsRatio of the areas of two trianglesSegment of altitude equal to the side of the triangleEqual sums of squares of parallelogram line segmentsPoint of concurrency and golden ratioRatio of areasPerpendicular linesIntersection point of three circlesSix points on conic sectionSix points on an ellipseSix concyclic pointsAn ellipse defined by vertices and orthocentersIntersection point of three circles IIIntersection point of three circles IIILine segments intersecting at the nine-point centerConstant sum of triangle areasFour concyclic pointsA generalization of Napoleon's theoremA generalization of constant chord theoremTwo triangles of equal areaAn equilateral triangle whose vertices are Fermat pointsThree concurrent line segmentsVariations on Napoleon's theoremConcyclic points in the plane of tangential quadrilateralIntersection point of three circles IVA generalization of butterfly theoremIntersecting secants of two congruent circlesTangent-secant theorem for two congruent circlesAn ellipse determined by circumcentersThree equilateral trianglesCharacterizations of cyclic quadrilateralsFour concyclic triangle centersFour concyclic triangle centers IIFour concyclic triangle centers IIIFour concyclic triangle centers IVFour concyclic triangle centers VFour concyclic triangle centers VIFive concyclic triangle centersFive concyclic triangle centers IIIntersection point of three circles VSeven concyclic triangle centersThree circles related to Conway's circlePoints of concurrency of the lines defined by triangle centers and verticesIsosceles triangle and excircleArea of bicentric quadrilateralArea of bicentric pentagonArea of bicentric hexagonCollinearity in bicentric pentagonCollinearity in bicentric hexagonParallelogram and lineConcyclicity in bicentric pentagonCollinearity in tangential pentagonFour orthocenters lie on a circleFive orthocenters lie on a circleSix orthocenters lie on a circleEight orthocenters lie on a circleCollinearity in bicentric pentagon IISix conelliptic pointsTriangle and lineParallelogram and line IIA variation on a theorem of VivianiA variation on a theorem of MorleyRatio of area of triangle and hexagonRatio of area of triangle and hexagon IICollinearity in bicentric heptagonCollinearity in bicentric octagonEqual sums of line segmentsEqual products of triangle areasThree pairs of similar trianglesFour pairs of similar trianglesPrincipal diagonals of octagon meet in a single pointConstant product of the lengths of two line segments