MathDB

3

Part of 2021 May Olympiad

Problems(2)

60, 30, 90 and + angles

Source: May Olympiad 2021 L2 #3

6/8/2021
Let ABCABC be a triangle and DD is a point inside of the triangle, such that ∠DBC=60∘\angle DBC=60^{\circ} and ∠DCB=∠DAB=30∘\angle DCB=\angle DAB=30^{\circ}. Let MM and NN be the midpoints of ACAC and BCBC, respectively. Prove that ∠DMN=90∘\angle DMN=90^{\circ}.
geometry
max no of Tuesday the 13th in a year (2021 May Olympiad L1 p3)

Source:

8/20/2021
In a year that has 365365 days, what is the maximum number of "Tuesday the 1313th" there can be?
Note: The months of April, June, September and November have 3030 days each, February has 2828 and all others have 3131 days.
algebra