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

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?

• Are Trignometric functions allowed ? – Anas Khaled Mar 24 at 15:34
• @AnasKhaled yes, but please don't do something that uses a calculator, as I'm trying to understand how to solve this question, without the use of a calculator – Michael Blane Mar 24 at 15:35
• There is insufficient information to determine the length of $DE$. – player3236 Mar 24 at 15:45
• Sorry, never mind, trig functions weren't necessary. – Anas Khaled Mar 24 at 15:48

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