A circle has a radius of 10 cm. A chord is 6 cm from the center. What is the length, in centimeters, of the chord?
Let O be the center of the circle.
Let the chord be labeled QR.
Draw a radius bisecting the chord at P.
Draw radii OQ and OR.
Now you have a right triangle OPQ with OP=6 and OQ (the hypotenuse) = 10.
So, PQ = 8 and the chord QR = 16
radius minus 6cm equals answer
10cm-6cm= answer
To find the length of the chord in a circle with a known radius and distance from the center, you can use the formula:
chord length = 2 * √(radius^2 - distance^2)
In this case, the radius is 10 cm and the chord is 6 cm from the center.
Substituting these values into the formula:
chord length = 2 * √(10^2 - 6^2)
chord length = 2 * √(100 - 36)
chord length = 2 * √(64)
chord length = 2 * 8
chord length = 16 cm
Therefore, the length of the chord is 16 cm.
To find the length of the chord, we can use the Pythagorean theorem.
Let's draw the circle and label the given information. The radius of the circle is 10 cm, and the chord is located 6 cm from the center.
* 10 cm - Radius
/ \
/ \
*-------* 6 cm - Distance from center to the chord
Now, let's draw a line from the center of the circle to one end of the chord, forming a right triangle.
|\
| \
10| \ 6
| \
| \
------
Chord
The line connecting the center of the circle to one end of the chord is the radius, which measures 10 cm. The distance from the center to the chord is given as 6 cm.
According to the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
In this case, we have:
6^2 + x^2 = 10^2
Simplifying:
36 + x^2 = 100
x^2 = 100 - 36
x^2 = 64
To solve for x, we take the square root of both sides:
x = √64
x = 8
Therefore, the length of the chord is 8 cm.