The radius of the circle centered at point O is 65 cm, the length of chord AB is 126 cm.Find the distance from chord AB

The radius of the circle centered at point O is 65 cm, the length of chord AB is 126 cm.Find the distance from chord AB to the tangent line k parallel to it

It is known from the properties of tangents that a segment drawn from the center of the circle to the point of tangency (radius) is perpendicular to the tangent. Since OK is perpendicular to the straight line k, it is perpendicular to the chord AB, since AB and k are parallel.
The perpendicular drawn from the center of the circle to the chord divides the chord in half, therefore: the point of intersection of AB and OK (i.e. H) divides AB into two equal segments:
AH = BH = AB / 2 = 126/2 = 63 cm.
Consider the triangle ANO: angle ANO = 90 degrees (since OH is a perpendicular), which means ANO is a right-angled triangle, OA = 65 cm – hypotenuse (since it lies opposite the right angle), AH = 63 cm and OH – legs.
By the Pythagorean theorem:
OH = √ (AO ^ 2 – AH ^ 2)
OH = √ (65 ^ 2 – 63 ^ 2) = √ (4225 – 3969) = √256 = 16 (cm).
The OK radius consists of two segments:
OK = OH + NK;
16 + NK = 65;
NC = 65 – 16;
NK = 49 cm.
NC is the distance from the chord AB to the straight line k.
Answer: NK = 49 cm.