MathDB

6

Part of 2014 ASDAN Math Tournament

Problems(5)

2014 Advanced #6

Source:

7/1/2022
Consider 77 points on a circle. Compute the number of ways there are to draw chords between pairs of points such that two chords never intersect and one point can only belong to one chord. It is acceptable to draw no chords.
2014Advanced Topics Test
2014 Algebra #6

Source:

7/8/2022
Compute cos⁡(π9)−cos⁡(2π9)+cos⁡(3π9)−cos⁡(4π9)\cos(\tfrac{\pi}{9})-\cos(\tfrac{2\pi}{9})+\cos(\tfrac{3\pi}{9})-\cos(\tfrac{4\pi}{9}).
2014Algebra Test
2014 General #6

Source:

7/4/2022
In triangle ABCABC, we have that AB=ACAB=AC, BC=16BC=16, and that the area of △ABC\triangle ABC is 120120. Compute the length of ABAB.
2014General Test
2014 Team #6

Source:

7/1/2022
Compute the largest integer NN such that one can select NN different positive integers, none of which is larger than 1717, and no two of which share a common divisor greater than 11.
2014team test
2014 Geometry #6

Source:

7/12/2022
Consider a circle of radius 44 with center O1O_1, a circle of radius 22 with center O2O_2 that lies on the circumference of circle O1O_1, and a circle of radius 11 with center O3O_3 that lies on the circumference of circle O2O_2. The centers of the circle are collinear in the order O1O_1, O2O_2, O3O_3. Let AA be a point of intersection of circles O1O_1 and O2O_2 and BB be a point of intersection of circles O2O_2 and O3O_3 such that AA and BB lie on the same semicircle of O2O_2. Compute the length of ABAB.
2014Geometry Test