In what cases is it impossible to draw a chord with a length of 13 cm in a circle of radius R?

Simply put, the largest chord in a circle is the diameter. Therefore, you can compare the diameter, which is equal to two radii, 2 * R, with the chord size of 13 cm. That is, the diameter must be greater than 13 cm. Or:

2 * R> 13 cm, or R> 6.5 cm.

Let us turn to the formula for the length of a chord l = 2 * R * sin (<A / 2), where A is the angle that encloses this chord. And the maximum is sin (<A / 2) = 1, then we return to the same equality, in which 2 * R min = 13, whence R min = 13/2 = 6.5 (cm).

Answer: A 13 cm chord cannot be drawn in a circle with a radius of less than 6.5 cm.