11.2. Given a right triangle $A B C$ with legs $A C=a$ and $C B=b$. Find a) the side of the square with vertex $C$ of the largest area, entirely lying within the triangle $A B C$; б) the dimensions of the rectangle with vertex $C$ of the largest area, entirely lying within the triangle $A B C$.
Answer. a) $\frac{a b}{a+b} ;$ b) $\frac{a}{2}$ and $\frac{b}{2}$. Solution. See problem 10.2