Question: For the the triangle $ABC$ , $BC=10$ and $AB=AC=13$. Given that $AD$ is a median and $BE$ is an altitude, find what $DE$ is equal to.
Well I construct the triable and I know that AD breaks BC into two equal parts of $5$. And that both $BE$ and $AD$ form right triangles.
If I look at triangle $BCE$, with angle $E$ being $90$ degrees, how can I say that $DE=DC=5=BD$
That's the answer, but I'm unsure as to why. I was leaning to thales theorem, where I can see $BDC$ as a diameter of a circle, that has angle $E$ being $90$ degrees. So they're all radius on the circle? Thus equal to 5?