Given right-angle triangle $\triangle ABC$$(\angle A=90^o)$, with $BC=10$ and $AC=6$. Circle is tangent to $BC$, goes through $A$ and intersects with $AB$ and $AC$ at the points $E$ and $D$ respectively. Find the length of $DE$.
I tried to solve this question as follows:
$AB=8$ from Pythagoras.
Since $DA\perp AE$ then $DE$ is diameter of the circle.
After drawing it out accurately, I see that $DE=4.8$, but I don't know how to work this out mathematically. Could you please explain to me how to solve this question?