$O$ is the centre of the circle. $AB$ is the chord and $D$ is mid-point of $AB$. If the length of $CD$ is $2\ cm$ and the length of chord is $12\ cm$, then what is the radius of the circle.

The line from the center to the midpoint of a chord is perpendicular to the chord, creating a right triangle with the radius as the hypotenuse. The half-length of the chord is 6 cm and the distance from the center to the chord is 8 cm (since CD is given as 2 cm, assuming it is the remaining part of the radius from the chord to the edge where the radius is 10 cm, meaning the distance calculation uses 8 cm). Using the Pythagorean theorem, the radius is calculated as the square root of 6 squared plus 8 squared, which equals the square root of 36 plus 64, giving a radius of 10 cm.

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