Distance of a chord AB of a circle from the center is 12cm and length of the chord is 10cm. Find the diameter of the circle.

Consider the figure,

Here, consider the property that the perpendicular from the centre of a circle to a chord bisects the chord.
Now, the distance of the cord from the centre of the circle is given by the perpendicular OC. Thus, the perependicular OC bisects the cord AB.
We know that the length of the cord AB is 10 cm.
So,
$$\begin{gathered} AC=\frac{AB}{2} \\ AC=\frac{10}{2} \\ AC=5 \end{gathered}$$

Next, using Pythagoras theorem in triangle OAC;
$$\begin{gathered} O{A}^2=A{C}^2+O{C}^2 \\ O{A}^2=5^2+{12}^2 \\ O{A}^2=25+144 \\ O{A}^2=169 \\ OA=\sqrt{169} \\ OA=13 \end{gathered}$$

Thus, the radius of the circle is 13 cm.

So,
Diameter = 2* radius
Diameter = 2*13
Diameter= 26

Therefore, the diameter of the circle is 26 cm