MathDB

1

Part of 2006 Oral Moscow Geometry Olympiad

Problems(2)

tangent at intersection of diagonals of a cyclic ABD parallel to a side

Source: 2006 Oral Moscow Geometry Olympiad grades 8-9 p1

10/17/2020
The diagonals of the inscribed quadrangle ABCDABCD intersect at point KK. Prove that the tangent at point KK to the circle circumscribed around the triangle ABKABK is parallel to CDCD.
(A Zaslavsky)
geometrytangentcyclic quadrilateral
construct line that divides a triangle into 2 polygons of equal circumradii

Source: 2006 Oral Moscow Geometry Olympiad grades 10-11 p1

10/20/2020
An arbitrary triangle ABCABC is given. Construct a line that divides it into two polygons, which have equal radii of the circumscribed circles.
(L. Blinkov)
equal circlesconstructiongeometryCyclic