Center C has a radius of 13.Chord AB=10. Find the distance from the center of the circle to chord AB. CD=?
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To find the distance from the center of the circle to chord AB, we can use the relationship between the radius, the chord, and the perpendicular distance from the center to the chord.
Since the chord AB is 10 units, we can draw a perpendicular line from the center C of the circle to the midpoint of AB. Let's call this point E. The line segment CE will be the distance from the center to the chord.
Now, we can use the Pythagorean theorem to find the length of CE. 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.
In our case, the length of CE is the hypotenuse, and the perpendicular distance from point E to chord AB is one of the other two sides. Let's call this distance x. The other side will be half the length of AB, which is 5 units.
Using the Pythagorean theorem, we have:
CE^2 = x^2 + 5^2
CE^2 = x^2 + 25
We also know that the length of CE is the radius of the circle, which is 13 units. So we can write:
13^2 = x^2 + 25
169 = x^2 + 25
Subtracting 25 from both sides of the equation, we get:
144 = x^2
Taking the square root of both sides, we have:
x = √(144)
x = 12
Therefore, the distance from the center of the circle to chord AB (CD) is 12 units.