In the interior of an equilateral triangle ABC a point P is chosen such that PA2 = PB2 + PC2. Find the measure of angle BPC.
Remember
"Four Bugs" or
"Three Bugs"?
In this problem, the six bugs start at the corners of a regular hexagon (with side length=10 inches).
Again, the bugs travel directly towards their neighbor (counter-clockwise). And, again, each bug homes in on its target, regardless of its target's motion. So, their paths will be curves spiraling toward the center of the hexagon, where they will meet.
What distance will the bugs have covered by then, and how did you determine it?
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