Trigonometry & Inverse Trigonometry
Triangle properties and exradii
Grade 11
Question:
<p>The minimum value of $\frac{r_1 r_2}{r_3}$ in a triangle is (symbols have their usual meaning)</p>
<p>(a) 1</p>
<p>(b) 3</p>
<p>(c) 8</p>
<p>(d) 27</p>
Step-by-Step Solution
Key Concept: Apply the relationship between exradii and optimize using AM-GM inequality to find the minimum value.
<p>Using the formula for exradii and optimization techniques, the minimum value of $\frac{r_1 r_2}{r_3}$ is 8.</p>
Correct Answer: C