MathDB

13

Part of 2021 AIME Problems

Problems(2)

omegalul

Source: 2021 AIME I Problem 13

3/11/2021
Circles ω1\omega_1 and ω2\omega_2 with radii 961961 and 625625, respectively, intersect at distinct points AA and BB. A third circle ω\omega is externally tangent to both ω1\omega_1 and ω2\omega_2. Suppose line ABAB intersects ω\omega at two points PP and QQ such that the measure of minor arc PQ^\widehat{PQ} is 120∘120^{\circ}. Find the distance between the centers of ω1\omega_1 and ω2\omega_2.
AMCAIMEAIME I2021 AIME Igeometrypower of a pointradical axis
Mod 1000

Source: 2021 AIME II #13

3/19/2021
Find the least positive integer nn for which 2n+5n−n2^n + 5^n - n is a multiple of 10001000.
AMCAIMEAIME II