A chord that is of length 18 cm is 12 cm away from the center of a circle. How far is a chord of length 10 cm from the center?
I know that chord of equal distance away are equidistant from the center but these are not of same length so I got a little stuck. Thank you :)
The length $l$ of a chord a distance $d$ away from the center of a circle of radius $r$ is $$l = 2{\sqrt{r^2-d^2}}$$ This can be demonstrated by the Pythagorean theorem: Length of a Chord
In your problem, you are given $l=18$ and $d=12$, so you can use this equation to find that $r=15$. You could also forgo the equation and find the radius of the circle by recognizing the Pythagorean triple (9, 12, 15) created by $r$, $d$, and half of $l$.
Now that you know the value of r, you can find the length of the chord when $d=10$ by using the equation again. You will find that $l=10{\sqrt 5}$.