MathDB

3

Part of 1998 Tuymaada Olympiad

Problems(1)

inequality with a segment that splits a triangle area in half and inradius

Source: Tuymaada 1998 p3

4/28/2019
The segment of length ℓ\ell with the ends on the border of a triangle divides the area of that triangle in half. Prove that ℓ>r2\ell >r\sqrt2, where rr is the radius of the inscribed circle of the triangle.
geometric inequalityinequalitiesinradiusarea of a triangleareageometry