CBSE Class 10 Maths (Standard) 2015 · Paper 30/1 · Question 6

In Figure 4, a triangle $ABC$ is drawn to circumscribe a circle of radius 3 cm, such that the segments $BD$ and $DC$ are respectively of lengths 6 cm and 9 cm. If the area of $△ABC$ is 54 cm${}^2$, then find the lengths of sides $AB$ and $AC$.