# geometry – Find \$ADcdot AF\$ when point \$C\$ is reflected across \$AD\$

$$ABC$$ is a triangle with side lengths $$AB=AC=20$$ and $$BC=18$$. $$D$$ is a point on $$BC$$ such that $$BD. $$C$$ is reflected across $$AD$$ and lands on $$E$$. $$EB$$ and $$AD$$ meet at $$F$$. Find $$ADcdot AF$$. No progress at all. This is my first question where I have seen points getting reflected and I really have no idea how to approach this question. Any help would be appreciated. Also is there any sort of “name” given to these categories of problems?

Edit: The question is indeed correct and the answer is $$400$$. But I have no clue how to get that value.

Here is a Geogebra diagram: (not completely accurate) https://www.geogebra.org/classic/hecrtmsd