tag:blogger.com,1999:blog-5541500.post1059492888453949236..comments2024-03-28T18:35:54.237+09:00Comments on BigHominid's Hairy Chasms: paradigm shift on the horizon?Kevin Kimhttp://www.blogger.com/profile/01328790917314282058noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5541500.post-45427024543555677112011-05-15T06:21:05.187+09:002011-05-15T06:21:05.187+09:00I figured it out, but I had to think for two or th...I figured it out, but I had to think for two or three minutes . . . which shows how rusty my math is since the question is really pretty basic.<br /><br />Jeffery Hodges<br /><br />* * *Horace Jeffery Hodgeshttps://www.blogger.com/profile/16684513618463766017noreply@blogger.comtag:blogger.com,1999:blog-5541500.post-47332526053955686972011-05-15T04:12:21.230+09:002011-05-15T04:12:21.230+09:00So, yeah-- the answer is A. In case the previous ...So, yeah-- the answer is A. In case the previous comment didn't make that clear.Kevin Kimhttps://www.blogger.com/profile/01328790917314282058noreply@blogger.comtag:blogger.com,1999:blog-5541500.post-11570593763354199852011-05-15T03:40:31.821+09:002011-05-15T03:40:31.821+09:00Solution to the Math Beast problem:
Imagine that ...Solution to the Math Beast problem:<br /><br />Imagine that points A, O, and D are the vertices of a triangle. We can immediately deduce that we're talking about an isosceles triangle because we know segments AO and DO are of equal length: they're the radii of Circle O.<br /><br />Knowing that Triangle AOD is an isosceles triangle, we know that Angle ODA must equal angle OAD, which is 65 degrees. Since the interior angles of a triangle add up to 180 degrees, the angle whose vertex lies at the center, Angle AOD, must equal 180-65-65, i.e., 180-130, or 50 degrees.<br /><br />Angle AOD is 50 degrees, and Angle COB is 40 degrees. Since arc length is proportional to the angles in question (the bigger the angle, the longer the arc), we can see that Minor Arc AD is longer than Minor Arc BC, because of the respective size of the angles in question (AOD and COB).<br /><br /><i>QED.</i>Kevin Kimhttps://www.blogger.com/profile/01328790917314282058noreply@blogger.com