The easy way:
The projection of on is . So .
The hard way:
Let be the intersection between and . As the triangle ABC is symmetric with respect to the line , every point on has a corresponding point on . So:
Note that as .
We need to find and . First, we find :
Now, we find . We can represent coordination in terms of .
Now compute :
Note that .
Let , and thanks to math.com:
(5) The same procedure can be applied to . Let be the expectation of given is located on , then: