Question 150
Let $A, B, C, D$ be points chosen on a circle, in that order. Line $BD$ is reflected over lines $AB$ and $DA$ to obtain lines $\ell_{1}$ and $\ell_{2}$ respectively. If lines $\ell_{1}, \ell_{2}$, and $AC$ meet at a common point and if $AB=4, BC=3, CD=2$, compute the length $DA$.