In a circle with a center o and a radius of 10 cm, a chord AB was drawn, the length of which is 12 cm.

In a circle with a center o and a radius of 10 cm, a chord AB was drawn, the length of which is 12 cm. What is the radius of the second circle with center O, which touches line AB?

The tangent AB forms a right angle with the radius OD drawn to the tangent point. Triangles ADO and BDO are rectangular. Since they have a common OD side, and the hypotenuses AO and BO are equal as the radii of one circle, the triangles ADO and BDO are equal.

Hence, AD = BD. Knowing the length AB, we find AD.

AD = AB / 2 = 12/2 = 6 cm.

The sum of the squares of the legs is equal to the square of the hypotenuse, that is, OD ^ 2 + AD ^ 2 = AO ^ 2.

OD ^ 2 = AO ^ 2 – AD ^ 2 = 12 * 12 – 10 * 10 = 44

OD = 2 √11