In a circle of radius $R$, a diameter is drawn and a point $A$ is taken on it at a distance $a$ from the center.

Find the radius of the circle that touches this diameter at point $A$ and touches the given circle internally.
Let $x$ be the desired radius.

By the Pythagorean theorem, $(R-x)^{2}=x^{2}+a^{2}$, from which $x=R^{2}-a^{2} / 2 R$.

![](https://cdn.mathpix.com/cropped/2024_05_06_0ef0b80dacb6d98eff5ag-11.jpg?height=417&width=435&top_left_y=1301&top_left_x=823)

## Answer

$R^{2}-a^{2} / 2 R$