Friday, December 10, 2010

Fox 316 and 318 - Solutions

Both solutions to 316 and 318 are by Bleaug. Also César Lozada has commented out a very similar solution to 316. Obviously, the maximum area is achieved when P is the mid-point, which is also the case for 321. But for Fox 322, it is not that obvious. That's why it still remains as unsolved. Thank you all for the good work.

Fox 316 Solution:
Bleaug:
"I couldn't get a pure geometric demonstration of these two problems. At best, with some lazy observations you are able to show that for both #316 and #318, maximum area is achieved for P midpoint of BC:
a) angle(QPR) in P remains constant when P varies
b) PR/PB is constant
c) PQ/PC is constantHence area(PQR) is proportional to PB.PC which is maximized when P is the midpoint of BC.
The rest is obtained by calculus."



Fox 318 Solution:

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