Sorry that the question seems confusing at first, since brilliant glitched and didn’t save my edits :/
Whole set
As in the figure, there are rays
.
. Let
be a rod which overlaps ray
. As ray
rotates
counter-clockwise
around point
at a speed of
per second, there are moments when one of
bisects the angle formed by the other two.
Denote time as in seconds. . If above scenario happens at , submit your answer as the product of all possible values of , in this example submit .
Assumptions:
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OC bisects at 50° / 2 = 25°, then OB bisects at 50° × 2 = 100° and finally OA bisects at 360° - 50° = 310°.
Answer
= [25° / (10° per second)] × [100° / (10° per second)] × [310° / (10° per second)]
= 2.5 × 10 × 31
= 775