Find the distance from the center of a circle of radius √17 to its chord, the length of which is 2.

Let’s connect the center of the circle with two segments to the ends of the given chord.

Consider the resulting triangle.

Since the two sides of this triangle are the radii of the circle, this triangle is isosceles and the required distance from the center of the circle to the chord will be equal to the height of this triangle, lowered to its base.

Since the base of the triangle is divided by its height in half, we can find the height of the triangle using the Pythagorean theorem:

√ ((√17) ^ 2 – (2/2) ^ 2) = √ ((√17) ^ 2 – 1 ^ 2) = √ (17 – 1) = √16 = 4.

Answer: the required distance is 4.