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The given data can be listed below,

Time dilation is the difference in the amount of time that has passed since an event according to several observers. Either gravity or relativistic velocity is responsible for this time dilation.

The beginning time must be 4 seconds since the signal will travel 4light seconds to reach clock A, whenthe time at the origin, for the initial synchronizing signal is$t=0$ .

Thus, the initial time set at clock A is $4s$.

The initial time must be 3 s since the signal must travel 3 light seconds to approach clock B when the time at origin, for the initial synchronizing signal is t=0.

Thus, the initial time set at clock B is $3s$.

The distance between the origin and clock A is 4 light-seconds, the distance between the origin and clock B is 3 light-seconds, so, the distance between the origin and clock C is

$\sqrt{4^2+3^2}light-second=5light-second$

Thus, the initial time set at clock C is $5s$.

The signal will take to reach the origin from the clock A. As the distance between the clock A and the origin is $4light-seconds$.

As the signal starts from clock A at $t=10s$, the time assigned by the observer, stationed at the origin, to the signal will be-

$$\begin{gathered} t^{\text{'}}=10s+4s \\ =14s \end{gathered}$$

Thus, the time assigned by the observer will be $t^{\text{'}}=14s$.