In a circle 2 chords AB and CD are drawn, intersecting at the point M, MB -10 = cm,

In a circle 2 chords AB and CD are drawn, intersecting at the point M, MB -10 = cm, AM = 12cm, DC = 23cm Find the length of CM and DM.

Since 2 chords are drawn in the circle and they intersect at point M, then AM * MB = CM * MD.

Further, we simply substitute the numbers and we get that:

12 * 10 = CM * MD = 120,

Since DC = 23 = CM + MD.

Let CM = x cm, then MD = 120 / x,

x + 120 / X = 23,

(x² + 120) / x = 23,

23 * x = x² + 120.

We solve the quadratic equation through the discriminant:

We get that x1 = 8, and x2 = 15,

if CM = 8, then MD = 23 – 8 = 15.

Answer: 8 and 15.