Let $A,B,C,D$ be the vertices of a four sided polygon taken in anti clockwise. Given $|AB|=|BC|=3,|AD|=|CD|=4,|BD|=5$ , Find $|AC|$ Let $A,B,C,D$ be the vertices of a four sided polygon taken in anti clockwise.
Given $$|AB|=|BC|=3,|AD|=|CD|=4,|BD|=5$$
Find $|AC|$
My try:I have noticed trangles $ABD$ and $BCD$ are right triangles but I do not know how to solve it.

You know the angle $C$ and $A$ are right and $BD$ must be perpendicular to $AC$(since the length of BC and AB are the same). Suppose the intersection point is $M$. Hence you can $AM$ by using BCM is similar to BDC.
