Find the chord length of a circle with a radius of 13 cm if the distance from the center of the circle to the chord is 12 cm.

Let’s complete the drawing. Let O be the center of the circle, AB – the chord, OK – the distance from O to AB (OK is perpendicular to AB). ОА = ОВ = 13 cm, OK = 12 cm.

The AOB triangle is isosceles (since OA = OB as the radii of a circle), it means that OK is not only the height, but also the median of the AOB triangle. Hence, AK = ВK.

In the ВOK triangle, the angle is K = 90 °, according to the Pythagorean theorem:

ВK = √ (BO² – KO²) = √ (13² – 12²) = √ (169 – 144) = √25 = 5 (cm).

Hence, AK = ВK = 5 (cm).

Therefore, AB = AB + BK = 5 + 5 = 10 (cm).

Answer: the chord length is 10 cm.