In a circle with a radius of 5 cm, a chord is drawn equal to 6 cm. Find the length of the segment

In a circle with a radius of 5 cm, a chord is drawn equal to 6 cm. Find the length of the segment connecting the center of the circle with the middle of the chord.

Let’s draw the diameter of the AD circle parallel to the BC chord and the radii of the OB and OC circle. The radii form an isosceles triangle BOS with the chord.

The height OH of an isosceles triangle is also its median, then BH = CH = BC / 2 = 6/2 = 3 cm.

The DOH triangle is rectangular, then OH ^ 2 = OB ^ 2 – BH ^ 2 = 25 – 9 = 16.

OH = 4 cm.

Answer: The distance from the center of the circle to the center of the chord is 4 cm.