# Scherzo

**Geometry**Level 4

The shorter chord is parallel to the diameter of the big circle as shown, and its shortest distance from the diameter is 24.

The line segment which is not a chord ends at the center of the circle and one end of the shorter chord.

A tangent of the two small circles is drawn ending at the points of tangency as shown.

Find the length of the tangent, which can be expressed as \(\frac{a\sqrt{b}}{c}\) in lowest terms, where \(a\), \(b\) and \(c\) are integers. Submit your answer as \(a+b+c\).