If the distance between center to chord is $12\text{ cm}$ and the length of the chord is $10\text{ cm}$, then the diameter of the circle is

1. A perpendicular line drawn from the center of a circle to a chord bisects the chord.Given the total chord length is $10\text{ cm}$, the length of half the chord is:
$$\text{Half-chord}=\frac{10}{2}=5\text{ cm}$$
The perpendicular distance from the center to the chord is given as $12\text{ cm}$. This forms a right-angled triangle where the radius ($r$) is the hypotenuse.Apply the Pythagorean theorem:
$$r^2=12^2+5^2$$
$$r^2=144+25=169$$
$$r=\sqrt{169}=13\text{ cm}$$
The diameter ($d$) of the circle is twice its radius:
$$d=2\times r=2\times 13=26\text{ cm}$$