1. **Problem statement:** Given that $CD=4$ and the perimeter of triangle $ABC$ is 23, find the perimeter of triangle $ABE$. 2. **Understanding the problem:** We have triangle $ABC$ with points $C$ and $D$ on side $AB$, and point $E$ connected to $D$ with a right angle at $D$. We know $CD=4$ and the perimeter of $ABC$ is 23. 3. **Key insight:** Since $C$ and $D$ lie on $AB$, segment $AB$ is divided into parts $AC$, $CD$, and $DB$. The perimeter of $ABC$ is $AB + BC + CA = 23$. 4. **Expressing $AB$:** Since $C$ and $D$ are on $AB$, $AB = AC + CD + DB$. But $C$ and $D$ are points on $AB$, so $AB = AC + CB$ (if $C$ is between $A$ and $B$), but here $D$ is between $A$ and $B$ as well, so $AB = AD + DB$ and $CD$ is a segment between $C$ and $D$ on $AB$. 5. **Perimeter of $ABE$:** Triangle $ABE$ has sides $AB$, $BE$, and $AE$. Since $E$ is connected to $D$ with a right angle at $D$, $DE$ is perpendicular to $AB$. 6. **Using right triangle $ADE$:** Since $DE$ is perpendicular to $AB$ at $D$, triangle $ADE$ is right-angled at $D$. The length $AE$ can be expressed as $AD + DE$ if $E$ lies off $AB$. 7. **Given data is insufficient to find exact lengths of $AE$ and $BE$ without additional information.** However, since the problem is from a figure and typical in such problems, the perimeter of $ABE$ equals the perimeter of $ABC$ minus $CD$ because $CD$ is replaced by $DE + CE$ in $ABE$. 8. **Assuming $E$ lies such that $BE + AE = BC + CD$ and $CD=4$, the perimeter of $ABE$ is:** $$\text{Perimeter of } ABE = \text{Perimeter of } ABC - CD = 23 - 4 = 19$$ **Final answer:** $$\boxed{19}$$