MathDB

3

Part of 2022 May Olympiad

Problems(2)

angle wanted, square and isosceles related

Source: 2022 May Olympiad L2 p3

9/4/2022
Let ABCDABCD be a square, EE a point on the side CDCD, and FF a point inside the square such that that triangle BFEBFE is isosceles and ∠BFE=90o\angle BFE = 90^o . If DF=DEDF=DE, find the measure of angle ∠FDE\angle FDE.
geometryangles
find digits for a sum

Source: 2022 May Olympiad L1 p3

9/5/2022
Choose nine of the digits from 00 to 99 and place them in the boxes in the figure so that there are no repeated digits and the indicated sum is correct. https://cdn.artofproblemsolving.com/attachments/6/2/7f06575ec70eb9ddd58c6cf9dd3cb60d306e7c.png Which digit was not used? You can fill in the boxes so that the unused digit is other?
number theory