### Theory:

Result $$5$$:
If two circles touch internally, the distance between their centres is equal to the difference of their radii.
Explanation:

If  two circles touch internally at a point $$B$$, then the distance $$OA$$ is equal to the difference of the radii $$OB$$ and $$AB$$.

$$\Rightarrow$$ $$OA$$ $$=$$ $$OB$$ $$-$$ $$AB$$
Proof for the result:
Let the two circles with centres $$O$$ and $$A$$ intersect each other internally at the point $$B$$.

Let the radius $$OB$$ $$=$$ $$r_{1}$$ and $$AB$$ $$=$$ $$r_{2}$$ and $$r_{1}$$ $$>$$ $$r_{2}$$.

Let distance between the centres be $$d$$.

$$\Rightarrow$$ $$OA$$ $$=$$ $$d$$

From the figure, we observe that $$OA$$ $$=$$ $$OB$$ $$-$$ $$AB$$.

$$\Rightarrow$$ $$d$$ $$=$$ $$r_{1}$$ $$-$$ $$r_{2}$$
Example:
Two circle with radii $$4$$ $$cm$$ and $$5$$ $$cm$$ intersect at a point $$O$$ internally. If so, find the distance between their centres.

Solution:

By the result, we know that:

Distance between the centres $$=$$ Difference of the radii.

Thus, the distance between the centres $$=$$ $$5$$ $$cm$$ $$-$$ $$4$$ $$cm$$

$$=$$ $$1$$ $$cm$$