Exercises

New/updated : xxx

Problems not so recreational...

Equilateral triangle "inscribed" in a square
2 circles in a rectangle
Pencil of conic sections type III (tangent to two given lines at given contact points).
Ellipses inscribed in a given rectangle.
Triangle with vertices on given lines and sides through given points.
Intersections constructible intersection of two conic sections.
Triangle given the intersections with circumcircle of...
Isosceles triangle given the inradius and one exradius.
Triangle given a relation from the angle bisector.
Half area A quadrilateral of half area in a triangle (Hyacinthos)
Ellipse from a circle with diameter AB (fr.sci.maths)
Searched circle through given P etc. (geometriagon)
Common tangent to a circle and a parabola.
Kiepert & Co geometric locii of isogonal conjugates.
Geometric locii related to inscribed equilateral triangles.
Half-perimeter Divide the perimeter of a triangle in two.
Chords points at given distance on two circles.
Segments equidistant points from two segments.
Centroids in a quadrilateral.
Affine triangle and triangle centers.
Steiner 1/7 triangle and Steiner ellipses.
Imaginary construction of imaginary intersection points.
Squares constructions with straightedge and squares only.
Triangle C = 2A Triangle with a double angle.
1/7 triangle The 'famous' 1/7 triangle.
Quadrilateral Construct a quadrilateral, given the sides and area.
Ellipse min ellipse containing given ellipse and given point.
Hyperscalene The most ordinary triangle.
Conic intersections Intersection points of two conic sections.
Pb#855 (geometriagon). Triangle DEF of maximal area circumscribed to ABC.
7 circles 7 circles touching a circle with radius R, one of them with same radius R.
Ceva and beyond. Parallel or concurrent lines and one circle.
Pentagon Disection of an irregular pentagon into a square
Polygon a strange relation in a regular polygon
Parabola Construct axis by paper folding
Tennis balls Pack 4 tennis balls in a cone
Half disc Cut an half disc in two equal area parts
Triangles Overlapping inscribed triangles
Ray Connect circle and ray by circle
Incircle Some property of incircle and cirumscribed quadrilaterals
Quadrilaterals Two similar cyclic quadrilaterals
5 circles Construct 5 touching circles
Miquel An extension to Miquel theorem

 

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