A circle is inscribed in a half circle with a diameter of \(\pi\) . What is the ratio of the area of the half circle to the area not covered by the inscribed circle?
the official answer say that the diameter of inscribed circle is \(\pi\)/2.
I wonder how do we know the diameter of inscribed circle is \(\pi\)/2.
Through research in the internet, there are many situations in which a circle inscribed other, but there diameter is not relating to each other.
Help me to find out what is wrong with my thought.