In a circle , the radius is 68 units and a chord of the circle is 120 units.

Part A)How far is the chord from the center?
Part B)Find the measure of the arc created by the chord.

Already asked and answered.

the Q is asked is if the shaded area between the cicles is 9picm,and the radius 4cm find the value of X.

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

Part A)
1. Draw a line from the center of the circle to one of the endpoints of the chord. This line is perpendicular to the chord and is known as the radius.
2. Divide the chord into two equal halves, creating a right triangle between the radius, the chord, and the line segment connecting the center of the circle and the midpoint of the chord.
3. Use the Pythagorean theorem to find the length of the line segment connecting the center of the circle and the midpoint of the chord.

Let's calculate it step by step.

Step 1:
Draw a line from the center of the circle to one of the endpoints of the chord. This line is perpendicular to the chord and is known as the radius. In this case, the radius is given as 68 units.

Step 2:
Divide the chord into two equal halves. We know that the chord is 120 units. So, each half of the chord is 120/2 = 60 units.

Step 3:
Since we have a right triangle, we can use the Pythagorean theorem to find the distance from the center to the chord.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's consider the radius as the hypotenuse, and the half of the chord as one side of the right triangle.

Using the Pythagorean theorem, we have:
radius^2 = (half of the chord)^2 + distance^2

Substituting the values we know:
68^2 = 60^2 + distance^2

Simplifying the equation:
4624 = 3600 + distance^2

Next, we can solve for the distance:

distance^2 = 4624 - 3600
distance^2 = 1024

Taking the square root of both sides:
distance = √1024
distance = 32 units

Therefore, the distance from the center of the circle to the chord is 32 units.

Now, moving on to Part B:

To find the measure of the arc created by the chord, we can use the following steps:

Part B)
1. Find the measure of the central angle that subtends the arc.
2. Use the formula to convert the central angle to the arc length.

Step 1:
The measure of the central angle can be found by using the formula:

Central angle = 2 * (arcsin((1/2) * (chord / radius)))

Plugging in the given values:
Central angle = 2 * (arcsin((1/2) * (120 / 68)))

We can use either a scientific calculator or lookup tables to find the value of arcsin.

Step 2:
To find the arc length, we can use the formula:

Arc length = (Central angle / 360) * 2 * π * radius

Plugging in the known values:
Arc length = (Central angle / 360) * 2 * π * 68

Simplifying this expression and substituting the value of the central angle:

Arc length = ((2 * (arcsin((1/2) * (120 / 68)))) / 360) * 2 * π * 68

Now, we can compute this expression to find the measure of the arc.