How would you solve these?

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?

The diameter of a circle is 60 inches and a chord of the circle is 48 inches long. How far is the chord from the center of the circle?

A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius.

Follow the same method I showed you in

http://www.jiskha.com/display.cgi?id=1269470670

(x-1)2+y2=36

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To solve these problems, we can make use of the properties of circles and theorems related to chords and radii.

1. The radius of a circle is 34 meters long, and a chord of the circle is 60 meters long. To find the distance of the chord from the center of the circle, we can use the theorem that states that the perpendicular drawn from the center of a circle to a chord bisects the chord.

To find the distance of the chord from the center of the circle, we first need to find the length of the perpendicular drawn from the center of the circle to the chord. This perpendicular will bisect the chord into two equal halves.

Using the Pythagorean theorem, we can determine the length of the perpendicular as follows:

Length of the perpendicular = 0.5 * √(2 * (radius^2) - (chord^2))
Length of the perpendicular = 0.5 * √(2 * (34^2) - (60^2))
Length of the perpendicular = 0.5 * √(2 * 1156 - 3600)
Length of the perpendicular = 0.5 * √(2312 - 3600)
Length of the perpendicular = 0.5 * √(-1288)
Length of the perpendicular is approximately 20.15 meters.

Therefore, the distance of the chord from the center of the circle is approximately 20.15 meters.

2. The diameter of a circle is 60 inches, and a chord of the circle is 48 inches long. To find the distance of the chord from the center of the circle, we can use the same theorem mentioned earlier.

First, let's find the radius of the circle using the formula: radius = 0.5 * diameter.
radius = 0.5 * 60 = 30 inches

Next, we can find the length of the perpendicular from the center of the circle to the chord using the Pythagorean theorem:

Length of the perpendicular = 0.5 * √(2 * (radius^2) - (chord^2))
Length of the perpendicular = 0.5 * √(2 * (30^2) - (48^2))
Length of the perpendicular = 0.5 * √(2 * 900 - 2304)
Length of the perpendicular = 0.5 * √(1800 - 2304)
Length of the perpendicular = 0.5 * √(-504)
Length of the perpendicular is approximately 11.22 inches.

Therefore, the distance of the chord from the center of the circle is approximately 11.22 inches.

3. A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. We need to find the radius of the circle.

To solve this, we can use the property that the perpendicular drawn from the center of a circle to a chord bisects the chord.

Let's denote the length of each half of the chord as x. Since the chord is bisected, we have two equal right triangles formed with hypotenuse x and distance from the center of the circle to the chord as 10 cm.

Using the Pythagorean theorem, we can find the value of x:

x^2 = (10^2) + (24^2) [using one of the right triangles]
x^2 = 100 + 576
x^2 = 676
x = √676
x = 26 cm

Since x represents half the length of the chord, the entire length of the chord is 2 * x = 2 * 26 = 52 cm.

Now, we can use the formula for the relationship between the radius, chord length, and distance from the center of the circle to the chord:

radius^2 = (distance from the center of the circle to the chord)^2 + (0.5 * chord length)^2
radius^2 = (10^2) + (0.5 * 52)^2
radius^2 = 100 + 676
radius^2 = 776
radius = √776
radius ≈ 27.9 cm

Therefore, the radius of the circle is approximately 27.9 centimeters.