Problem 45. Through the given point $K$, draw a circle that is tangent to the given circle at the given point $T$ on it.
Construction instruction. Extend $K T$ until it intersects the given circle at point $E$ (Fig.35). Draw the diameter $E F$ of the given circle. Through point $K$, draw a line parallel to $E F$ and extend $F T$ until it intersects this line at point $N$. Then

![](https://cdn.mathpix.com/cropped/2024_05_21_c833ac06d3d78911cbb1g-036.jpg?height=591&width=591&top_left_y=1735&top_left_x=1109)

35
$\mathrm{KN}-$ is the diameter of the desired circle.