A circle is inscribed in a right – angled triangle with legs of length 5 and 12.

Given a right-angled triangle with legs 5 cm and 12 cm.
Hypotenuse $= 13$ cm.

Inradius:
$r = \frac{5 + 12 - 13}{2} = 2$ cm

The radii to the tangent points on the two legs are perpendicular to the legs.
These radii (each of length $2$) together with the corner at the right angle form a square-like quadrilateral, whose sides are equal to the inradius.

So, the quadrilateral formed has side $r = 2$.

Area $= r^2 = 2^2 = 4$

Answer: $4 \text{ square units}$ (4 वर्ग इकाइयाँ)