The diameter of the AB-circle with center O intersects the chord CD at point M. Find the chord CD

The diameter of the AB-circle with center O intersects the chord CD at point M. Find the chord CD if CM = 8 cm, AM = 6 cm, OB = 11 cm.

For the solution we use the properties of the chords of the circle.

By the property of the chords of a circle that intersect at one point, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

AM * BM = CM * DM.

By condition, AM = 6 cm, ОВ = 11 cm, then, since ОВ = ОА = R = 11 cm, then ОМ = ОА – АМ = 11 – 6 = 5 cm, and ВМ = ОВ + ОМ = 11 + 5 = 16 cm.

Then, 6 * 16 = 8 * DM.

DM = 96/8 = 12 cm.

СD = CM + DM = 8 + 12 = 20 cm.

Answer: The СD chord has a length of 20 cm.