3. 20 The circumcenter of the triangle, it can be known that $\triangle A B C$ is an isosceles triangle, i.e., $\mathrm{BA}=\mathrm{BC}$. Therefore, $f(1)=f(3)$, and it is easy to know that there are 20 such triangles.
3. Given the sets $M=\{1,2,3\}, N=\{1,2,3,4,5\}$, define the function $f: M \rightarrow N$. Let points $A(1, f(1)), B(2, f(2)), C(3, f(3)), \triangle A B C$ have the circumcenter $D$, and $\underset{D A}{\operatorname{mu}}+D C=\lambda D B(\lambda \in R)$. Then the number of functions $f(x)$ that satisfy the condition is $\qquad$.