1. Identify the centers and radii of the circles:
- Let the centers of circles $k_1, k_2, k_3$ be $O_1, O_2, O_3$ respectively.
- The radii of the circles are $a, b, c$ respectively, with $a > c > b$.

2. Position the circles:
- Since the circles are tangent to the line $d$ at points $A, B, C$ respectively, and $k_1$ is tangent to $k_2$, and $k_2$ is tangent to $k_3$, the distances between the centers of the circles are $O_1O_2 = a + b$ and $O_2O_3 = b + c$.

3. Tangent line properties:
- The tangent line to $k_3$ at $E$ is parallel to $d$ and meets $k_1$ at $D$. This implies that $DE$ is a horizontal line parallel to $d$.

4. Perpendicular line properties:
- The line perpendicular to $d$ at $A$ meets line $EB$ at $F$. This implies that $AF$ is vertical.

5. **Calculate $AF$:**
- Since $AF$ is vertical and $F$ lies on $EB$, we need to find the vertical distance from $A$ to $F$.
- Given that $AF \parallel CE$, we can use similar triangles to find $AF$.

6. Use similar triangles:
- Consider the triangles formed by the centers and the points of tangency. The vertical distance from $A$ to the line $d$ is $a$, from $B$ to $d$ is $b$, and from $C$ to $d$ is $c$.
- Since $AF \parallel CE$, the triangles $\triangle AFO_1$ and $\triangle CEO_3$ are similar.

7. **Calculate $AF$ using similar triangles:**
- The ratio of the sides of the similar triangles is given by the ratio of the radii:
$$\frac{AF}{CE} = \frac{a}{c}$$
- Since $CE = 2c$ (as $E$ is a point on the circle $k_3$ and the tangent line is parallel to $d$), we have:
$$AF = 2c \cdot \frac{a}{c} = 2a$$

8. **Calculate $AD$:**
- Let $G$ be the point where $AO_1$ meets $DE$. Since $DE$ is parallel to $d$, $G$ is the midpoint of $DE$.
- The distance $AD$ can be calculated using the Pythagorean theorem in the right triangle $\triangle AOD$:
$$AD = \sqrt{AG^2 + OD^2 - OG^2}$$
- Given $AG = 2c$, $OD = a$, and $OG = 2c - a$, we have:
$$AD = \sqrt{(2c)^2 + a^2 - (2c - a)^2}$$
$$AD = \sqrt{4c^2 + a^2 - (4c^2 - 4ac + a^2)}$$
$$AD = \sqrt{4ac}$$
$$AD = 2\sqrt{ac}$$

9. Conclusion:
- Since $AF = 2a$ and $AD = 2\sqrt{ac}$, we need to verify if $2a = 2\sqrt{ac}$.
- Simplifying, we get:
$$a = \sqrt{ac}$$
$$a^2 = ac$$
$$a = c$$
- This contradicts the given condition $a > c$. Therefore, there must be an error in the initial assumptions or calculations.