MathDB

6

Part of 2024 JHMT HS

Problems(2)

Median is an Element

Source:

9/7/2024
Compute the number of nonempty subsets SS of {1,2,3,4,5,6,7,8,9,10}\{ 1,2,3,4,5,6,7,8,9,10 \} such that the median of SS is an element of SS.
combinatorics2024
Altitudes, Midpoints, and Similar Triangles

Source:

9/8/2024
Let N5N_5 be the answer to problem 5.
Triangle JHUJHU satisfies JH=N5JH=N_5 and JU=6JU=6. Point XX lies on HU‾\overline{HU} such that JX‾\overline{JX} is an altitude of △JHU\triangle{JHU}, point YY is the midpoint of JU‾\overline{JU}, and JX‾\overline{JX} and HY‾\overline{HY} intersect at ZZ. Assume that △HZX\triangle{HZX} is similar to △JZY\triangle{JZY} (in this vertex order). Compute the area of △JHU\triangle{JHU}.
geometrysimilar triangles2024