MathDB

8

Part of 2024 JHMT HS

Problems(2)

Concyclic Points and Angle Bisectors

Source:

9/7/2024
Points AA, BB, CC, and DD lie on a circle Γ\Gamma, in that order, with AB=5AB=5 and AD=3AD=3. The angle bisector of ∠ABC\angle ABC intersects Γ\Gamma at point EE on the opposite side of CD↔\overleftrightarrow{CD} as AA and BB. Assume that BE‾\overline{BE} is a diameter of Γ\Gamma and AC=AEAC=AE. Compute DEDE.
geometryangle bisectorcircumcircle2024
Coloring Sides of a Regular Polygon

Source:

9/8/2024
Let N7N_7 be the answer to problem 7.
Each side of a regular N7N_7-gon is colored with a single color from a set of two given colors. Two colorings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. Compute the number of possible different colorings.
combinatorics2024