B2. The diagonals of a rhombus are $10 \mathrm{~cm}$ and $24 \mathrm{~cm}$. What is the length of the radius of the inscribed circle of the rhombus?
B2. On the sketch of the rhombus, we mark point $E$, which is the intersection of the diagonals. The diagonals intersect perpendicularly and bisect each other. Triangle $A B E$ is a right triangle with side lengths $5 \mathrm{~cm}, 12 \mathrm{~cm}$, and $13 \mathrm{~cm}$. The area of this triangle is $30 \mathrm{~cm}^{2}$. We conclude that the height to side $A B$ in this triangle measures $\frac{60}{13} \mathrm{~cm}$ and that this height is also the radius of the inscribed circle.

On the sketch of the rhombus, the marked point $E$ is the intersection

![](https://cdn.mathpix.com/cropped/2024_06_07_bce9c6e2a6f4f88bb0deg-14.jpg?height=402&width=628&top_left_y=784&top_left_x=1274)
of the diagonals

Conclusion:

the diagonals of the rhombus bisect each other and are perpendicular...............................................................

Triangle $A B E$ is a right triangle .......................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_bce9c6e2a6f4f88bb0deg-14.jpg?height=54&width=1639&top_left_y=1418&top_left_x=274)

Conclusion:

the height to side $A B$ in this triangle measures $\frac{60}{13} \mathrm{~cm} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

Conclusion:

This height is also the radius of the inscribed circle

1 point