MathDB

4

Part of 2015 Danube Mathematical Competition

Problems(2)

prove that the rectangle is a square, double angle is given

Source: Danube 2015 Junior P4

9/8/2018
Let ABCDABCD be a rectangle with AB≥BCAB\ge BC Point MM is located on the side (AD)(AD), and the perpendicular bisector of [MC][MC] intersects the line BCBC at the point NN. Let Q=MN∪AB{Q} =MN\cup AB . Knowing that ∠MQA=2⋅∠BCQ\angle MQA= 2\cdot \angle BCQ , show that the quadrilateral ABCDABCD is a square.
geometryrectangleperpendicular bisectoranglessquare
Nice problem

Source:

9/5/2017
Given an integer n≥2n \ge 2 ,determine the numbers that written in the form a1a_1a2a_2++a2a_2a3a_3++......ak−1a_{k-1}aka_k , where kk is an integer greater than or equal to 2, and a1a_1 ,... aka_k are positive integers with sum nn.
number theory