1. **Problem statement:** We have a circle with radius $5$ cm and a chord of length $6$ cm. We need to find the area of another circle concentric with the first one that is tangent to this chord. 2. **Understanding the problem:** The new circle shares the same center as the original circle but has a different radius. It is tangent to the chord, meaning the chord touches the new circle at exactly one point. 3. **Key formula:** The distance from the center of the circle to the chord is given by $$d = \sqrt{r^2 - \left(\frac{c}{2}\right)^2}$$ where $r$ is the radius of the original circle and $c$ is the chord length. 4. **Calculate the distance from center to chord:** $$d = \sqrt{5^2 - \left(\frac{6}{2}\right)^2} = \sqrt{25 - 9} = \sqrt{16} = 4 \text{ cm}$$ 5. **Radius of the new circle:** Since the new circle is tangent to the chord, its radius equals the distance from the center to the chord, which is $4$ cm. 6. **Calculate the area of the new circle:** $$\text{Area} = \pi r^2 = \pi \times 4^2 = 16\pi \text{ cm}^2$$ **Final answer:** The area of the concentric circle tangent to the chord is $16\pi$ cm$^2$.