10. (12 points) As shown in the figure, $A$ and $B$ are the two endpoints of a diameter of a circular track. Three miniature robots, Jia, Yi, and Bing, start moving simultaneously on the circular track at a uniform speed. Jia and Yi start from $A$, and Bing starts from $B$; Yi moves clockwise, while Jia and Bing move counterclockwise. After 12 seconds, Jia reaches $B$, and after another 9 seconds, Jia catches up with Bing for the first time, which is also when Jia meets Yi for the first time; when Bing first reaches $A$, it will take another $\qquad$ seconds for Yi to reach $B$ for the first time.
【Solution】Solution: After 12 seconds, person A reaches from $A$ to $B$, then after another 9 seconds, A reaches point $C$, and the length of $BC$ is equal to $\frac{3}{4}$ of the length of $AB$, so the length of $AC$ is equal to $\frac{1}{4}$ of the length of $AB$,

In 21 seconds, the distance covered by A is $AB + BC = \frac{7}{4} AB$, the distance covered by B is $AC = \frac{1}{4} AB$, and the distance covered by C is $BC = \frac{3}{4} AB$, thus the speed ratio of A: B: C $=7: 1: 3$, the time taken for C to travel from $C$ to $A$ $=21 \times \frac{1}{3}=7$ (seconds), at this time, B travels from point $C$ to point $D$, taking 7 seconds as well, since $CA = \frac{1}{3} BC$, then $CD = \frac{1}{3} AC$, so $CB = 8 CD$, the time required for B to reach $B$ after C reaches $A$: $8 \times 7=56$ (seconds). Therefore, the answer is: 56