document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158190>Question 1158190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify that A = (7, 4), B = (−7, 4), C = (−1, −8), and D = (8, −1) all lie on a circle centered at the origin. Let K be the intersection of chords AC and BD. Prove that triangles KAB and KDC are similar and find the ratio of similarity. Then, show that KA · KC = KB · KD.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781118 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) For each of the points, the distance from the origin is sqrt(65).<br><BR>\n" );
document.write( "(2) Angles A and D are congruent because they both cut off arc BC; angles B and C are congruent because they both cut off arc AD.  Two pairs of congruent angles makes the triangles similar.<br><BR>\n" );
document.write( "(3) The lengths of corresponding sides AB and CD are 14 and sqrt(130), so the ratio of similarity is 14:sqrt(130).<br><BR>\n" );
document.write( "(4) KA*KC = KB*KD by the theorem about the lengths of the pieces of two intersecting chords.  Or you can prove it using the two similar triangles.<br><BR>\n" );
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