MathDB

2

Part of 2008 Chile National Olympiad

Problems(1)

existence of a triangle with sides PA \sqrt2, PB,PC Chile 2008 L2 P2

Source:

5/31/2019
Let ABCABC be right isosceles triangle with right angle in AA. Given a point PP inside the triangle, denote by a,ba, b and cc the lengths of PA,PBPA, PB and PCPC, respectively. Prove that there is a triangle whose sides have a length of a2,ba\sqrt2 , b and cc.
right triangleisoscelesTrianglegeometry