MathDB

Geometric inequality with radii

Source: Russian TST 2014, Day 11 P1 (Group NG), P3 (Groups A & B)

January 8, 2024

geometryInequality

Problem Statement

Let

R{}

and

r{}

be the radii of the circumscribed and inscribed circles of the acute-angled triangle

ABC{}

respectively. The point

M{}

is the midpoint of its largest side

BC.

The tangents to its circumscribed circle at

B{}

and

C{}

intersect at

X{}

. Prove that

\frac{r}{R}\geqslant\frac{AM}{AX}.