92. Given a right triangle with sides 9, 12, 15. Find the diameter of the circle inscribed in this triangle.

## Problems of Marcus Junius Nipsus.

From the Erfurt Codex.
92. Solution: $A B=A E+R ; A E=A D$,

$$
B C=F C+R ; F C=D C
$$

therefore,

$$
A B+B C=2 R+A C
$$

from which

$$
2 R=A B+B C-A C
$$

in this case

$$
2 R=9+12-15=6
$$

![](https://cdn.mathpix.com/cropped/2024_05_21_926f0bb262c8f9569516g-096.jpg?height=291&width=460&top_left_y=1579&top_left_x=1209)

Fig. 33.

The Erfurt Codex is a manuscript of later origin (possibly from the 11th century), representing a collection of excerpts, sometimes more complete than the Arzeryan Codex: it contains a series of stereometric problems that are almost absent in ancient lists.

Marcus Junius Nipsus (lived no later than the 2nd century). Roman writer - surveyor.