The following circle has the diameter of 10cm, what is the distance from any of the small circles to the edge of the main circle?

Question

Note : This is a question from a currently obsolete source(http://stopbeingbullied.org/geoimg.jpg), therefore I have to edit the entire question.

Let $O$ be the center of a circle of diameter $10$ m and let $AB$ be a chord of this circle with $AB=6$m. Let $C$ be the midpoint of $AB$ and let the line joining $O$ and $C$ intersect the circle at $D$, where $D$ and $O$ are on opposite sides of $AB$. The task is to find the length of $CD$.

Answer 1

Again is it only pythagoras theorem.

Answer 2

Let the line be $AB$, and the center $O$.

Draw a line from $O$ to the midpoint of the chord, call it $C$. This line is also perpendicular to the chord. Extend this line to the circumference of the circle, let it intersect at $D$. We want to find $CD$.

So, we can use the Pythagoras theorem on the triangle $AOC$. Note that $\angle OCA = 90$, hence $OC^2 + CA^2 = OA^2$. Now, $OA=5$, and since $C$ is the midpoint, $CA = 3$. Hence, $OC^2 = 25-9=16$, and $OC=4$. Finally, $DC = OD-OC = 5-4=1$.