I tried to do this problem but the answer doesn't jive. Circle C has a radius of 13. Chord AB is 10. Find the distance from the center of the circle to chord AB which is labeled CD. I labeled CD = x. 1/2 of AB = 5. The line segment CB (13) is the same os CD (x). I tired x sq + 5 sq = 13 sq and got. Answer I got was 12. What is wrong?
Nothing is wrong. The chord is 12 units from the center of the circle.
To find the distance from the center of circle C to chord AB, you can use the Pythagorean theorem.
First, let's draw a diagram to visualize the problem:
```
C
/ \
/ \
/_____\ (circle C)
/ \
/ \
A_________B
```
Let's label the center of the circle as O. We need to find the length of CD (x), which is the perpendicular distance from the center of the circle to chord AB.
To solve this, we will use the property that the perpendicular drawn from the center of a circle to a chord bisects the chord.
So, in this case, CD is equal to half the length of AB, which is 5.
To represent this mathematically: CD = 1/2 * AB
So, CD = 1/2 * 10 = 5.
Therefore, the value of x (CD) is 5, not 12.
Your mistake in your calculation was that you squared the lengths of x, 5, and 13 separately, rather than considering that x is equal to 5.
To find the value of x using the Pythagorean theorem, you would set up the equation:
x^2 + 5^2 = 13^2
x^2 + 25 = 169
x^2 = 144
x = √144
x = 12
Since CD is already known to be 5 (from the bisected chord), the correct answer is x = 5, not x = 12.