MathDB

7

Part of 2019 Tuymaada Olympiad

Problems(2)

computational for juniors in Tuymaada , tangent circle given

Source: Tuymaada Olympiad 2019 juniors p7

7/22/2019
A circle ω\omega touches the sides AAB and BCBC of a triangle ABCABC and intersects its side ACAC at KK. It is known that the tangent to ω\omega at KK is symmetrical to the line ACAC with respect to the line BKBK. What can be the difference AK−CKAK -CK if AB=9AB = 9 and BC=11BC = 11?
geometrytangentcircle
An inequality on grid cell

Source: Tuymaada 2019 P7 out of 8

7/15/2019
NN cells chosen on a rectangular grid. Let aia_i is number of chosen cells in ii-th row, bjb_j is number of chosen cells in jj-th column. Prove that ∏iai!⋅∏jbj!≤N! \prod_{i} a_i! \cdot \prod_{j} b_j! \leq N!
inequalitiesgrid