OPM 2017

Determine all integer values of n for which the number $\frac{14n+25}{2n+1}$ 'is a perfect square.

In triangle $[ABC]$ , the bisector in $C$ and the altitude passing through $B$ intersect at point $D$ . Point $E$ is the symmetric of point $D$ wrt $BC$ and lies on the circle circumscribed to the triangle $[ABC]$ . Prove that the triangle is $[ABC]$ isosceles.

Let $[ABCD]$ be a convex quadrilateral with $AB = 2, BC = 3, CD = 7$ and $\angle B = 90^o$ , for which there is a inscribed circle. Determine the radius of this circle.