The diameter of the CD is perpendicular to the chord AB. The radius forms an angle of 45 ° with the chord.

The diameter of the CD is perpendicular to the chord AB. The radius forms an angle of 45 ° with the chord. The distance from the center to the chord is 7 cm. Find the length of the chord.

Since, according to the condition, the chord AB is perpendicular to the diameter of the СD, the triangle OCH is rectangular, in which, according to the condition, the angle OВН = 450, then the triangle is isosceles, OH = BH = 7 cm.
In right-angled triangles OНВ  and OНA, the leg OH is common, and the hypotenuse OA = OB = R, then the triangles OHB and OHA are equal in leg and hypotenuse, and then AH = BH = 7 cm.
AB = AH + BH = 7 + 7 = 14 cm.
Answer: The chord length is 14 cm.