MathDB

7

Part of 2017 Tuymaada Olympiad

Problems(2)

Line crossing triangles

Source: Tuymaada 2017 Junior Level

7/18/2017
An equilateral triangle with side 2020 is divided by there series of parallel lines into 400400 equilateral triangles with side 11. What maximum number of these small triangles can be crossed (internally) by one line?
Tuymaada 2017 Q7 Juniors
combinatorics
Tuymaada 2017 Seniors Q7

Source: Tuymaada 2017 Seniors Q7 (day 2 P3)

9/26/2017
A point EE lies on the extension of the side ADAD of the rectangle ABCDABCD over DD. The ray ECEC meets the circumcircle ω\omega of ABEABE at the point F≠EF\ne E. The rays DCDC and AFAF meet at PP. HH is the foot of the perpendicular drawn from CC to the line ℓ\ell going through EE and parallel to AFAF. Prove that the line PHPH is tangent to ω\omega.
(A. Kuznetsov)
tangentrectanglegeometry