MathDB

4

Part of 2015 Online Math Open Problems

Problems(2)

2014-2015 Spring OMO #4

Source:

4/14/2015
Find the sum of all distinct possible values of x2−4x+100x^2-4x+100, where xx is an integer between 1 and 100, inclusive.
Proposed by Robin Park
Online Math Open
2015-2016 Fall OMO #4

Source:

11/18/2015
Let ω\omega be a circle with diameter ABAB and center OO. We draw a circle ωA\omega_A through OO and AA, and another circle ωB\omega_B through OO and BB; the circles ωA\omega_A and ωB\omega_B intersect at a point CC distinct from OO. Assume that all three circles ω\omega, ωA\omega_A, ωB\omega_B are congruent. If CO=3CO = \sqrt 3, what is the perimeter of △ABC\triangle ABC?
Proposed by Evan Chen
Online Math Open