Question 5
In sector $AOB$, the chord $AB$ has length 18 cm. $OA$ and $OB$ are tangent to both circles, and arc $AB$ is tangent to the circle with centre $C$. The circle with centre $C$ has radius 6 cm. Find the radius, in centimetres, of the circle with centre $D$.
As depicted, the two circles are externally tangent, their centres lie on the angle bisector, and the larger circle is internally tangent to the sector arc. The drawing is not to scale.
As depicted, the two circles are externally tangent, their centres lie on the angle bisector, and the larger circle is internally tangent to the sector arc. The drawing is not to scale.