The Tilt of a Triangle

★ 7/10plane geometry inequality Casework Triangle Geometry

Problem

For a triangle with sides $a \leqslant b \leqslant c$ , define its tilt

t = \max\left\{\frac{a}{b}, \frac{b}{c}, \frac{c}{a}\right\}\cdot\min\left\{\frac{a}{b}, \frac{b}{c}, \frac{c}{a}\right\}.

1. Find the tilt of an isosceles triangle. 2. If $a = 1$ , find the range of possible values of $t$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, inequality, Casework, Triangle Geometry

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