Given right-angle triangle $\triangle ABC$ $(\angle A=90^o)$, with $BC=10$ and $AC=6$. Find the length of $DE$.

Question

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?

Answer 1

The diagrams below shows that there is simply insufficient information to determine the length of $DE$.