The radius of a circle is 34 meters long,and a chord of the circle is 60 meters long.how far is the chord from the center of the circle?

draw a diagram and you should see an isosceles triangle with sides 34, 34 and 60

draw the height from the centre to the 60 side
it will hit the middle, so now you have a right-angled triangle with sides h, 30 and hypotenuse 34

solve for h
h^2 + 30^2 = 34^2

Sixteen

To find the distance of the chord from the center of the circle, we can use the following formula:

Distance = √(Radius^2 - (0.5 * Chord length)^2)

Given:
Radius = 34 meters
Chord length = 60 meters

Using the formula, we can substitute the values and calculate:

Distance = √(34^2 - (0.5 * 60)^2)
= √(1156 - 900)
= √256
= 16 meters

Therefore, the chord is 16 meters away from the center of the circle.

To find the distance of the chord from the center of the circle, we can use the theorem that states that the perpendicular bisector of a chord passes through the center of the circle.

Let's start by drawing a sketch of the problem to visualize it better.

We have a circle with a radius of 34 meters. Inside the circle, we have a chord with a length of 60 meters. We want to find the distance from the center of the circle to the chord.

First, let's split the chord in half, which creates two segments, each with a length of 30 meters (half of the chord length).

Next, we draw a line from the center of the circle to the midpoint of the chord, which is perpendicular to the chord. This line is called the perpendicular bisector.

Now, we have a right-angled triangle formed by the radius, the perpendicular bisector, and half of the chord.

The radius is 34 meters, half of the chord is 30 meters, and we want to find the distance from the center to the chord, which we'll call 'd'.

Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, we can write the equation as follows:

d^2 = 34^2 - 30^2

Simplifying:

d^2 = 1156 - 900
d^2 = 256

Taking the square root of both sides:

d = √256
d = 16

Therefore, the distance from the center of the circle to the chord is 16 meters.