MathDB

3

Part of 1997 Hungary-Israel Binational

Problems(2)

Hungary-Israel Binational 1997_3

Source:

11/4/2008
Let ABC ABC be an acute angled triangle whose circumcenter is O O. The three diameters of the circumcircle that pass through A A, B B, and C C, meet the opposite sides BC BC, CA CA, and AB AB at the points A1 A_1, B1 B_1 and C1 C_1, respectively. The circumradius of ABC ABC is of length 2P 2P, where P P is a prime number. The lengths of OA1 OA_1, OB1 OB_1, OC1 OC_1 are integers. What are the lengths of the sides of the triangle?
geometrycircumcirclegeometry unsolved
Hungary-Israel Binational 1997_6

Source:

11/4/2008
Can a closed disk can be decomposed into a union of two congruent parts having no common point?
geometrycircumcirclegeometric transformationrotationsymmetrytopologycombinatorics unsolved