MathDB

2

Part of 2014 Czech-Polish-Slovak Junior Match

Problems(2)

a + b + 4 = 4\sqrt{a\sqrt{b}}

Source: Czech-Polish-Slovak Junior Match 2014, Individual p2 CPSJ

3/13/2020
Solve the equation a+b+4=4aba + b + 4 = 4\sqrt{a\sqrt{b}} in real numbers
equationalgebra
circumcenter equidistant from 2 points wanted, parallelogram related

Source: Czech-Polish-Slovak Junior Match 2014, Team p2 CPSJ

3/23/2020
Let ABCDABCD be a parallelogram with ∠BAD<90o\angle BAD<90^o and AB>BCAB> BC . The angle bisector of BADBAD intersects line CDCD at point PP and line BCBC at point QQ. Prove that the center of the circle circumscirbed around the triangle CPQCPQ is equidistant from points BB and DD.
geometrycircumcircleparallelogramequal segments