MathDB

2

Part of 2020 New Zealand MO

Problems(2)

midpoint of XY lies on diagonal BD of square ABCD (2020 NZMO 1.2)

Source:

1/10/2021
Let ABCDABCD be a square and let XX be any point on side BCBC between BB and CC. Let YY be the point on line CDCD such that BX=YDBX = YD and DD is between CC and YY . Prove that the midpoint of XYXY lies on diagonal BDBD.
midpointsquaregeometry
min N = 5mod7, 8 mod6, 9 mod7

Source: 2020 New Zealand MO Round 2 p2 NZMO

9/22/2021
Find the smallest positive integer NN satisfying the following three properties. ∙\bullet N leaves a remainder of 55 when divided by 77. ∙\bullet N leaves a remainder of 66 when divided by 8 8. ∙\bullet N leaves a remainder of 77 when divided by 99.
number theoryremainder