Dont forget to Euclid your work to show got to the answers for full credit. :P (Rimshot)
On Fri, Mar 6, 2015 at 9:33 AM, Steve Smith <[email protected]> wrote: > Shawn - > > Good to hear from you stranger! > > I'm pretty confident in my solution, I'm not sure why the program doesn't > acknowledge it. Do you (or anyone) see any problem with it? > > The method was > > 1. construct an arbitrary line segment OP through B spanning the circle > 2. construct a parallel line segment MQ to OP through A > 3. construct rays OM and PQ to find homothetic center R > 4. construct circles of radius RA and RB centered on R > 5. find intersections of each circle at S and T and U and T > 6. construct rays through RUT and RVS to match the criteria > > steps 4 and 5 could delete one of the two substeps as redundant. > > not sure how GeoGebra actually determines a match with their own > "solution". > > Hi Robert, Steve, > > One way to arrive at a solution is to make a third circle with radius r2 > - r1 (https://en.wikipedia.org/wiki/Tangent_lines_to_circles, under > external tangents). This reduces the problem to finding a tangent to a > point outside of the new circle ( > https://en.wikipedia.org/wiki/Thales%27_theorem, bottom figure for > instance). Since the tangent is invariant to this type of transformation, > you can scale your solution to the original circles. Interesting game; > thanks for posting. > > > Shawn > > > On Sun, Mar 1, 2015 at 11:43 PM, Steve Smith <[email protected]> wrote: > >> I am also stuck at 23, but I'm not sure it is from lack of success... >> RVS and RUT "should" match the criteria (using your homothetic centers >> "R" hint). >> >> >> >> >> >> I had at least one other approach which *also* failed to "pass". I'm a >> little unclear on how the "snap to grid" and/or "snap to intersection" >> works, which *might* be bolloxing things up? >> >> I'm wondering if *anyone* else took your bait? I ripped through these >> "pretty fast" stumbling on 16 I think for a little extra time. >> >> I have to confess I got stuck at Level 23 because, I'm claiming, I wasn't >> familiar with the geometry of homothetic centers >> <http://en.wikipedia.org/wiki/Homothetic_center>. Is there a complexity >> site that does the same sort of thing? It looks like a great way to extend >> one's education on an otherwise relatively difficult subject. >> >> Robert C >> >> On 2/27/15 2:54 PM, Robert J. Cordingley wrote: >> >> A new but possibly entertaining productivity sink? >> http://euclidthegame.com >> >> Robert C >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> >> >> >> >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> >> >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> > > > > This body part will be downloaded on demand. > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >
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