MathDB

2

Part of 2009 May Olympiad

Problems(2)

angle chasing with convex ABCD, equailateral ABD, isosceles BCD, <C=90^o

Source: May Olympiad (Olimpiada de Mayo) 2009 L2

9/11/2018
Let ABCDABCD be a convex quadrilateral such that the triangle ABDABD is equilateral and the triangle BCDBCD is isosceles, with ∠C=90o\angle C = 90^o. If EE is the midpoint of the side ADAD, determine the measure of the angle ∠CED\angle CED.
geometryAngle ChasingisoscelesEquilateral Triangleconvex quadrilateral
p+q^2+r^3=200 diophantine in primes

Source: XV May Olympiad (Olimpiada de Mayo) 2009 L1 P2

9/22/2022
Find prime numbers p,q,rp , q , r such that p+q2+r3=200p+q^2+r^3=200. Give all the possibilities.
Remember that the number 11 is not prime.
number theorydiophantineDiophantine equation