Can be solved by most 13-year-olds in China‘-2

Geometry Level 3

Sorry that the question seems confusing at first, since brilliant glitched and didn’t save my edits :/


Whole set
Carefully read assumptions before answering\small \color{#D61F06} \text{Carefully read assumptions before answering}
As in the figure, there are rays OA,OB,OCOA,OB,OC. BOC=50\angle BOC=50^\circ. Let OAOA be a rod which overlaps ray OCOC. As ray OAOA rotates counter-clockwise around point OO at a speed of 1010^\circ per second, there are moments when one of OA,OB,OCOA,OB,OC bisects the angle formed by the other two.
It rotates COUNTER-CLOCKWISE :) It rotates COUNTER-CLOCKWISE :)

Denote time as tt in seconds. 0t360\le t\le 36. If above scenario happens at t=1,t=2,t=3t=1,t=2,t=3, submit your answer as the product of all possible values of tt, in this example submit 1×2×3=61\times 2\times 3=6.

Assumptions:

  • There is no angle greater than 180180^\circ or less than 00^\circ. No angle equals 180180^\circ or 00^\circ.
    • This must be explained further:
    • Here OCOC bisects AOB\angle AOB while ODOD is not considered as a bisector at all.
  • Angle bisectors are rays. Rays, straight lines and line segments are to be STRICTLY DISTINGUISHED FROM ONE ANOTHER.
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