Problems(2)
no B created by removing middle digit of no A, divisible by 2018
Source: : Czech-Polish-Slovak Junior Match 2018, individual p4 CPSJ
2/1/2020
Determine the smallest positive integer with an odd number of digits and this property, that both and the number created by removing the middle digit of the number are divisible by .
number theorydivisibleDigit
circumencter lies on perp. bisector, equilateral and 3 circumcircles related
Source: Czech-Polish-Slovak Junior Match 2018, Team p4 CPSJ
3/7/2020
A line passing through the center of the equilateral triangle intersects sides and , respectively, in points and . Circumcircles of triangle and intersects, besides point , also at point . Prove that the center of circumcircle of triangle lies on the perpendicular bisector of the segment .
geometrycircumcirclecolinearCircumcenter