The solution provided appears to assume the tangent points are across from each other (second image). What is stopping the circle from being tangent at two adjacent points (first image, diagram on the right)?
Thank you!
Can the second condition be satisfied?
Assuming your question is rhetorical, I take it that the half-area statement necessarily implies the tangent points are opposite to each other. I am struggling with the intuition here though. Any guidance?
You kind of show it in your example - can you come up with an example where the circle is tangent to only two sides?