tag:blogger.com,1999:blog-6933544261975483399.post2451113174618420294..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1001: Triangle, Circumcircle, Perpendicular, Perpendicular Bisector, Tangent, Collinear PointsAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6933544261975483399.post-21054896438049922092014-06-04T21:45:19.494-07:002014-06-04T21:45:19.494-07:00Be is a diameter of circumcircle of triangle ABCBe is a diameter of circumcircle of triangle ABCPeter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-10063354383775328422014-06-04T10:30:05.295-07:002014-06-04T10:30:05.295-07:00Triangle (BAE) ... What is E?Triangle (BAE) ... What is E?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-86576487345214774822014-05-23T16:33:01.653-07:002014-05-23T16:33:01.653-07:00BD is the altitude from B of triangle ABC . D is o...BD is the altitude from B of triangle ABC . D is on ACPeter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-8350742087005275282014-05-23T03:24:10.297-07:002014-05-23T03:24:10.297-07:00sorry what Dsorry what DAnonymoushttps://www.blogger.com/profile/14208563219141512109noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-29687396866154264542014-04-06T23:55:47.270-07:002014-04-06T23:55:47.270-07:00Let O is the center of the circle
Let the tangent ...<br />Let O is the center of the circle<br />Let the tangent at B cut P1P2 at P<br />We have ∆ (BDC) ~ ∆ (BAE)<br />And ∆ (BP1O)~ ∆ (BCA)~ ∆ (BOP2)<br />So BO and BP are angle bisectors of angle P2BP1.<br />Since ∆ (P3CP1) similar to ∆ (P3AP2) => P3P1/P3P2= CP1/AP2 … (1)<br />Since BP is an angle bisector => PP1/PP2= P1B/BP2….. (2)<br />Compare (1) and (2) and note that P1B=P1C and P2A=P2B <br />We have P3P1/P3P2= PP1/PP2 => P coincide to P3 => P1,P2,P3 are collinear<br />Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.com