Hello, realintegerz!

Find the radius of a circle that is inscribed in a right triangle

whose short sides are 27 and 36 units long. Code:

A *
| \
| \
| \
| \
| \
| \
| * * * \ 45
| * *
| * *
27 |* o *\
| o r \
* P o * \
* o o o o * * \
* r o * \
| o \
|* o r * \
| * o * \
| * o * \
B * - - - * * * - - - - - - - - - - - - * C
36

We have right triangle

. . Using Pythagorus, we have: .

The area is: . .[1]

The inscribed circle has center and radius .

Draw line segments

. . and we have three smaller triangles.

. . Area of

. . Area of

. . Area of

The total area is: . .[2]

We just described the area of in two ways.

Equate [1] and [2]: .