Explanation:

- In a right-angled triangle, the radius (r) of the inscribed circle can be found using the formula: $r=\frac{a+b-c}{2}$, where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

- Here, the legs are 5 cm and 12 cm.

- The hypotenuse $c$ is calculated using the Pythagorean theorem: $c=\sqrt{5^2+{12}^2}=13$.

- Substituting in the formula: $r=\frac{5+12-13}{2}=\frac{4}{2}=2$.

Option 1: 2

- This option is correct based on the calculations.

- Option 2: 2.8 is incorrect.

- Option 3: 2.5 is incorrect.

- Option 4: 3 is incorrect.

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