Finding a diagonal in a trapezoid given the other diagonal and three sides The figure below is a trapezoid, what is the length of the red line?
Thank you very much in advance!


There are 2 circles, one of radius $49$ , with center $(0,0)$the other with radius $28$ with center $(49,0)$, solving the system:
$$x^2+y^2=49^2$$
$$(x-49)^2+y^2=28^2$$
Gives you the intersection point $(41,12\sqrt{5})$. Then you solve the system
$$y=12\sqrt{5}$$
$$(x-49)^2+y^2=28^2$$
and cuts the circle with radius $28$ at $x=57$, but we have also $y=12\sqrt{5}$ so the lenght is $\sqrt{57^2+(12\sqrt{5})^2}=63$
