A problem of forming equal angles in plane geometry

Question

$C$ and $D$ are two points on the same side of a straight line $AB$. Find a point $X$ on $AB$ such that $\angle CXA = \angle DXB$.

Answer 1

then construct it as

• draw line d perpendicular to AB line from D
• E is the intersection of line d and AB
• draw circle C1, centre at E trough D
• F is the intersection of C1 and line d
• draw line e between C and F
• the intersection of e and AB is point X