BODY { margin:0px; } #education_m { text-align:left; width:1081px; background-color:#ffffff; } #education_nar { text-align:left; width:697px; background-color:#ffffff; padding:17px; } #banner { background-color:#333333; padding:10px; border-bottom:#003366 5px solid; } #banner td { font-size:23px; color:#cccccc; font-family:Arial, serif; width:1081px; } #banner td.title{ padding-left:0px; font-size:13pt; } #footer { background-color:#333333; padding:5px; font-size:12px; color:#cccccc; border-top:#003355 5px solid; } #education_m, #education_nar { font-family:Arial, serif; font-size:9pt; color:#000000; } #education_a { margin-top:15px; margin-bottom:30px; padding-left:5px; border-left:#666666 5px solid; } #education_l { width:1081px;; background-color:#E0E0E0; color:#000000; padding:8px; padding-right:0px; padding-left:0px; border-bottom:#999999 1px solid; } font.de { color:#333333; line-height:17px; } a:link, a:hover, a:active, a:visited { font-size:10pt; color:#003399; font-family:Arial, serif; } #education_l a{ font-size:10pt; text-decoration:none; color:#333333; padding-left:15px; } #education_l a:hover{ text-decoration:underline; } #footer a{ font-size:10pt; text-decoration:none; color:#cccccc; padding-left:0px; padding-right:15px; } #footer a:hover{ text-decoration:underline; } #education_text { text-align:justify; } #education_text a{ font-size:9pt; text-decoration:none; color:#000000; padding-left:0px; } #education_text a:hover{ text-decoration:underline; } #education_li a{ font-size:10pt; text-decoration:underline; color:#000000; padding-left:0px; } #education_li a:hover{ text-decoration:underline; } #education_li1 { font-size:8pt; color:333333; padding-left:7px; } #header { font-size:20px; color:003366; } #right { vertical-align:top; float:right; width:200px; margin-top:50px; } #b { padding:5px; padding-left:20px; background-color:#eeeeee; width:100%; border-bottom:#999999 1px solid; padding-top:9px; } html { height: 100%; overflow: auto; } #header0 { font-size:20px; color:003366; } #header1 { font-size:14px; color:003366; } #education_li2 { font-size:8pt; color:333333; padding-left:7px; }

 

Problem 675: Quadrilateral, 45 and 90 Degrees, Circumcircles, Intersecting Circles, Secant, Collinear Points. Level: High School, College, Math Education.

The drawing shows the quadrilateral ABCD with the exterior angles B and D equal to 45 degrees. Point E is on AB extended, such that angle DCE = 90 degrees, and point F is on AD extended, such that angle BCF = 90 degrees. CIrcumcircle O of triangle ABD and circumcircle O' of triangle AEF meet at G. CG meets circle O at H. Prove that points A, O, and H are collinear. 

Intersecting Circles, Collinear Points, 45 and 90 degrees
 

 

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