The chord length of the circle is 30, and the diameter of the circle itself is 34. Find the distance from the center of the circle to the chord.

if you draw the radii to the chord in the place where it intersects with the circle, you get a triangle (it is isosceles, since its sides are radii, and they are equal in the circle). we draw a height in this triangle, which will be both the median and the bisector (by the property of an isosceles triangle). this height is the distance from the center of the circle to the chord, that is, what we need to find. we use the Pythagorean theorem: The radius (which will be the median) is equal to half the diameter, equal to 17 cm. one of the legs of this triangle is equal to half of the chord (since the second leg is the median of the chord), the first leg is 15 cm. to find the second cathet, you need to use the Pythagorean theorem : the square of the hypotenuse is equal to the sum of the squares of the legs, therefore, the second leg = 289-225 = 64, root 64 = 8, therefore the second leg = 8cm = the distance from the center of the circle to the chord.
ANSWER: 8 cm