1. **State the problem:** We have a circle with radius $14$ cm and two chords $AB$ and $CD$ with lengths $12$ cm and $10$ cm respectively. We need to find the distance of each chord from the center of the circle. 2. **Formula and rules:** The distance $d$ from the center of the circle to a chord of length $c$ in a circle of radius $r$ is given by the formula: $$d = \sqrt{r^2 - \left(\frac{c}{2}\right)^2}$$ This comes from the right triangle formed by the radius, half the chord, and the distance from the center to the chord. 3. **Calculate distance for chord AB:** $$d_{AB} = \sqrt{14^2 - \left(\frac{12}{2}\right)^2} = \sqrt{196 - 6^2} = \sqrt{196 - 36} = \sqrt{160} = 4\sqrt{10} \approx 12.65 \text{ cm}$$ 4. **Calculate distance for chord CD:** $$d_{CD} = \sqrt{14^2 - \left(\frac{10}{2}\right)^2} = \sqrt{196 - 5^2} = \sqrt{196 - 25} = \sqrt{171} \approx 13.08 \text{ cm}$$ **Final answer:** - Distance of chord AB from center is approximately $12.65$ cm. - Distance of chord CD from center is approximately $13.08$ cm.