tag:blogger.com,1999:blog-2400513859305780710.post3526552957701343552..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Just Practice. Topic: All. Level: AIME/Olympiad.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-2400513859305780710.post-52704554004402237422005-12-05T20:11:31.000-08:002005-12-05T20:11:31.000-08:00I know #4, too lazy to post solution, so I"ll...I know #4, too lazy to post solution, so I"ll give you a question from my mock AIME in progress instead (I'll probably change it later):<br><br>Triangle ABC has AB = 13, BC = 37. Point D is on AC such that BD = \sqrt{193}. Point E is on BC such that BE = 10. AE and BD intersect at point F. CF intersects AB at point G. If \frac{AG}{BG} = \frac{70}{81}, find the area of triangle ABC.<br><br>(This is #8 so far :) )QCnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-33582599355435210212005-12-05T21:30:19.000-08:002005-12-05T21:30:19.000-08:00Well I have an ugly solution, aka Stewart's+Ce...Well I have an ugly solution, aka Stewart's+Ceva to find the length of AC, then Heron's...paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-89202897962211464992005-12-05T21:36:36.000-08:002005-12-05T21:36:36.000-08:00Stewart's + Ceva is the solution I intended, b...Stewart's + Ceva is the solution I intended, but the last step can be done slightly more simply by drawing the altitude from B to AC. :)QCnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-40853789240670454582005-12-05T22:54:54.000-08:002005-12-05T22:54:54.000-08:00Haha ic. I assume it turns out much more nicely th...Haha ic. I assume it turns out much more nicely than it looks, probably thanks to all those ugly numbers given in the problem.paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-29655088980904239602005-12-06T17:40:57.000-08:002005-12-06T17:40:57.000-08:00QC, do you have an AoPS username?QC, do you have an AoPS username?chess64noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-66811371452745621462005-12-06T22:54:16.000-08:002005-12-06T22:54:16.000-08:00QC = t0rajir0uQC = t0rajir0upaladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-50972988214230388322005-12-07T12:54:00.000-08:002005-12-07T12:54:00.000-08:00Oh.Oh.chess64noreply@blogger.com