# The radius of the circle centered at point O is 85, the length of the chord AB is 80. Find the distance from the chord AB to the tangent k parallel to it Draw the segment OB as shown in the figure.
The distance from the chord AB to the tangent k parallel to it is denoted as CD.
CD = OC + OD, OC is the radius of the circle, find OD.
By the condition of the problem, k || AB. CD is perpendicular to k (by the tangent property), then CD is perpendicular to AB (since CD is secant for parallel lines, and the internal cross-angles are equal), then the triangle OBD is right-angled.
DB = AB / 2 = 80/2 = 40 (according to the second property of the chord)
OB is equal to the radius of the circle.
Then by the Pythagorean theorem:
OB2 = OD2 + DB2
85 ^ 2 = OD ^ 2 + 40 ^ 2
7225 = OD ^ 2 + 1600
OD ^ 2 = 7225-1600 = 5625
OD = 75
CD = OC + OD = 85 + 75 = 160 Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.