For the general case, it is useful to remember that AY will always be equal to AP. Same observation for BP and BX. It is then obvious that the perimeter of the triangle must be equal to 20 when we reorganize aforementioned segments onto the two long tangent lines.

south_korea_ln

Because we can choose P at random between X and Y, i choose it to be at X. This gives me a completely flattened out triangle where one of the sides has collapsed to a length of 0. The two other sides are equal to 10, hence the perimeter is equal to 20.

Thanks for posting this, i likely won't post many daily puzzles this week, but will pick up the pace again next week.

science

Two tangents from point $$C$$ are drawn to a circle. $$\overline{YC} = \overline{XC} = 10$$.

Point $$P$$ is randomly chosen on the circle between $$X$$ and $$Y$$. $$\overline{AB}$$ is tangent to the circle in $$P$$.

What's the length of the perimeter of the triangle $$ABC$$? 

![puzzle3](https://i.ibb.co/3Fgxy83/puzzle3.png)
