Excuse me if I am misunderstanding something basic, but what does inscribe mean? Does it not mean that the smaller circle is just completely inside the half-circle (touching all sides possible) (Not necessarily in the centre). So, when I read the question, I can't figure where this smaller circle is exactly.
As per my understanding, we can have infinite circles inscribed in the half-circle, touching all sides of the half-circle at various points, with of course, the biggest one in the centre.
Please see attached image.
So, why have we assumed that its centre is on the radius of the half circle?
I'm taking this post from another poster but I never saw the question answered and was wondering if someone could give an explanation. I know that a circle inscribed in a polygon has each side of the polygon tangent to the circle. But when a circle is inscribed in a semicircle, how do we know where the circle is placed. In the figure drawn by the above poster, is each circle shown considered to be "inscribed?
For more context, this question is in reference to the test question below:
A circle is inscribed in a half circle with a diameter of π. What is the ratio of the area of the half circle to the area not covered by the inscribed circle?
A. 1: 1
B. 1: 2
C. 1: 4
D. 3: 4
E. 2: 1