fall-2017-final

HEXA Cha l l enge

Problems created by: Dr. Oscar Tagiyev

October Challenge: In the triangle ABC, angle C is obtuse. The side AB equals x cm. A circle goes through points A, B, and the point of intersection of the heights (orthocenter) of the triangle ABC. Find the radius of such circle.

November Challenge: There are a total N amount of nuts in all three pockets. What is the probability that each pocket contains the same amount of nuts ( N /3)?

December Challenge: Everyone is aware of the murderer-waves, tsunamis, that are able to move in the ocean at a tremendous rate. They can break and turn over ships and/or vessels. Estimate the propagation rate of the tsunami wave near the coastline, where the water depth is about 100 meters.

Virginia Mathematics Teacher vol. 44, no. 1

30