tag:blogger.com,1999:blog-6933544261975483399.post7857557636955332759..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1094: Tangent Circles, Tangent Chord, Radius, Sagitta of ArcAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6933544261975483399.post-70840476869618366362021-01-18T10:01:30.848-08:002021-01-18T10:01:30.848-08:00Geometry solution :No Pythagoras , by similarity a...Geometry solution :No Pythagoras , by similarity and the power of a point<br />https://photos.app.goo.gl/AT5Kee5YWYq6dBdf8c.t.e.o.https://www.blogger.com/profile/16937400830387715195noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-32816416463980660382015-11-16T02:57:04.187-08:002015-11-16T02:57:04.187-08:00Geometry solution
O,Q,T are collinear
OQ^2 = MD...Geometry solution<br /><br />O,Q,T are collinear <br /><br />OQ^2 = MD^2 + (QD-OM)^2<br /><br />So { (a-b)/2}^2 + (r-R+c)^2 = (R-r)^2.......(1)<br /><br />Applying Pythagoras to Tr. AOM<br /><br />(R-c)^2 + {(a+b)/2}^2 = R^2...,,,(2)<br /><br />(2) -(1) and simplifying using the difference of 2 squares <br /><br />ab + r(2R-2c-r) = 2rR -r^2<br /><br />Which further simplifies to <br /><br />ab = 2cr<br /><br />Sumith Peiris<br />Moratuwa<br />Sri Lanka<br /><br /> Sumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-66754896604867671242015-03-09T06:16:34.706-07:002015-03-09T06:16:34.706-07:00Thanks Pravin. It's MCD, and ab=2cr (lower cas...Thanks Pravin. It's MCD, and ab=2cr (lower case). Jacob HA (EMK2000)https://www.blogger.com/profile/17238561555526381028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-73939845069890654112015-03-08T20:18:25.019-07:002015-03-08T20:18:25.019-07:00A typo I think
It should be CD=c/cos∠MCD
(ab = 2cr...A typo I think<br />It should be CD=c/cos∠MCD<br />(ab = 2cr of course)Pravinhttps://www.blogger.com/profile/05947303919973968861noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-32144183860379242542015-03-08T14:04:08.941-07:002015-03-08T14:04:08.941-07:00Observe that CDT are collinear,
thus ab=CD×DT.
...Observe that CDT are collinear, <br />thus ab=CD×DT. <br /><br />Now since<br />CD=c/cos∠MDT<br />DT=2r cos∠QDT<br /><br />Hence, ab=2CR. Jacob HA (EMK2000)https://www.blogger.com/profile/17238561555526381028noreply@blogger.com