# The segments AB and CD are the chords of a circle. Find the distance from the center of the circle to the chord CD, if AB = 12

The segments AB and CD are the chords of a circle. Find the distance from the center of the circle to the chord CD, if AB = 12, CD = 16, and the distance from the center of the circle to the chord AB is 8 Draw the segments OB and OC, as shown in the figure.
The distance from a point to a line is the length of the perpendicular drawn to the line. Therefore, OE is perpendicular to AB, and OF is perpendicular to CD. Points E and F divide their chords in half (by chord property)
It turns out that the triangles OEB and OCF are rectangular, EB = AB / 2 and CF = CD / 2.
By the Pythagorean theorem:
OB ^ 2 = OE ^ 2 + EB ^ 2
OB ^ 2 = 8 ^ 2 + (12/2) ^ 2
OB ^ 2 = 64 + 36 = 100
OB = 10
OB = OC = 10 (since OB and OC are the radii of a circle)
By the Pythagorean theorem:
OC2 = CF2 + FO2
OC ^ 2 = (CD / 2) ^ 2 + FO ^ 2
10 ^ 2 = (16/2) ^ 2 + FO ^ 2
100 = 64 + FO2
Fo ^ 2 = 36
Fo = 6
Answer: the distance from the center of the circle to the CD chord is 6 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.