TAILIEUCHUNG - Collection of all geometric world champion P3

On one of the given lines take segment AB and construct its midpoint, M (cf. Problem ). Let A1 and M1 be the intersection points of lines PA and PM with the second of the given lines, Q the intersection point of lines BM1 and MA1. It is easy to verify that line PQ is parallel to the given lines. In the case when point P does not lie on line AB, we can make use of the solution of Problem . If point P lies on line AB, then we can first drop perpendiculars l1 and l2 from some other points. | SOLUTIONS 201 . On one of the given lines take segment AB and construct its midpoint M cf. Problem . Let A1 and M1 be the intersection points of lines PA and PM with the second of the given lines Q the intersection point of lines BM1 and MA1. It is easy to verify that line PQ is parallel to the given lines. . In the case when point P does not lie on line AB we can make use of the solution of Problem . If point P lies on line AB then we can first drop perpendiculars l1 and l2 from some other points and then in accordance with Problem draw through point P the line parallel to lines 11 and l2. . a Let A be the given point l the given line. First let us consider the case when point O does not lie on line l. Let us draw through point O two arbitrary lines that intersect line l at points B and C. By Problem in triangle OBC heights to sides OB and OC can be dropped. Let H be their intersection point. Then we can draw line OH perpendicular to l. By Problem we can drop the perpendicular from point A to OH. This is the line to be constructed that passes through A and is parallel to l. In order to drop the perpendicular from A to l we have to erect perpendicular l to OH at point O and then drop the perpendicular from A to . If point O lies on line l then by Problem we can immediately drop the perpendicular l from point A to line l and then erect the perpendicular to line l from the same point A. b Let l be the given line A the given point on it and BC the given segment. Let us draw through point O lines OD and OE parallel to lines l and BC respectively D and E are the intersection points of these lines with circle S . Let us draw through point C the line parallel to OB to its intersection with line OE at point F and through point F the line parallel to ED to its intersection with OD at point G and finally through point G the line parallel to OA to its intersection with l at point H. Then AH OG OF BC . AH is the segment to be .

• Toán học
• Algebraic problems on the triangle inequality
• Inequalities of areas
• quadrilateral’s diagonals
• Miscellaneous problems on the triangle inequality
• The quadrilateral
• 4 node quadrilateral element
• Center point based discrete shear gap
• Discrete shear gap
• Four node quadrilateral element
• Reissner–Mindlin plate theory
• BMC Musculoskeletal Disorders
• Acetabular fracture
• Quadrilateral plate
• Screw placement
• Digital measurement
• Acetabular fractures
• Virtual surgical planning
• Patient specific implants
• 3D printing patient specific plates
• Quadrilateral plate disruption
• quadrilateral cross section
• Thin walled FG beam
• Higher order coupling
• Beam frame modal
• Thin walled FG sandwich beams
• Limit analysis
• Bearing capacity factors
• Strip footing
• Estimation bearing capacity factors
• Bubble enhanced quadrilateral finite element
• Pink Cubes aka pink Towe
• Invite the child or group of children
• Points of Interest
• Brown quadrilateral prisms aka brown stairs
• English learning materials
• Finite element method
• Triangular element
• Quadrilateral element
• Free vibration analysis
• Stress analysis
• Aero elastic analysis
• Fracture fixation
• Epidemiological investigations
• Post traumatic arthritis
• Minimally invasive
• Anatomical plate
• Pararectus approach
• Lecture Finite element method
• Basis equation of plane problem
• Finite element discretization
• Quadrilateral plane element
• Triangular plane element
• Bimaterial interface crack
• Consecutive interpolation procedure
• Discontinuous problems
• Consecutive interpolation finite element method
• Enrichment functions