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.

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.


  • 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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