"Through an intersection point of two circles, draw a secant such that its segment inside the given disks is congruent to a given length.
Hint: Construct a right triangle whose hypotenuse is the segment between the centers of the given disks,
and one of the legs is congruent to a half of the given length".
Let's say segment EF is given and we have to construct secant through point K such that its length inside disks A and B equals segment EF.
Many thanks for any ideas or suggestions.
Best Answer
Hint:
$ACSR$ is a rectangle. Do you see why $AC=RS=\frac12 LM$?