document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252997>Question 252997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove that common internal tangent segments of two circles are congruent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185491 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This might be a bit wild to explain via description, but here we go . . .<BR>\n" );
document.write( "First, draw two circles and call the left one center (A) and the right one center (B).<BR>\n" );
document.write( "Second, draw to internal tangents. One tangent touches (B) at point x and it touches (A) at point y. The second tangent touches (B) at point q and touches (A) at point p. <BR>\n" );
document.write( "Third, where the two tangents cross, call that point e.<BR>\n" );
document.write( "We are now ready to prove.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "STATEMENT 1: two circles, A and B that are internally tangent at point e, and touch a at Y and p as well as touch B at x and q.<BR>\n" );
document.write( "REASON 1: given<BR>\n" );
document.write( "STATEMENT 2: Ay congruent to Ap; Bq congruent to Bx.<BR>\n" );
document.write( "REASON 2: definition of radii<BR>\n" );
document.write( "STATEMENT 3: angle Aye, angle Ape, angle Bqe, and angle Bxe are all right angles<BR>\n" );
document.write( "REASON 3: definition of tangent line<BR>\n" );
document.write( "STATEMENT 4: Ae congruent Ae ; Be congruent Be<BR>\n" );
document.write( "REASON 4: reflexive property of equality<BR>\n" );
document.write( "STATEMENT 5: triangle Ape congruent triangle Aye ; triangle Bqe congruent triangle Bxe<BR>\n" );
document.write( "REASON 5: HL postulate<BR>\n" );
document.write( "STATEMENT 6: ey congruent ep ; eq congruent ex<BR>\n" );
document.write( "REASON 6: CPCTC<BR>\n" );
document.write( "STATEMENT 7: ye + ex = yx ; pe + eq = pq<BR>\n" );
document.write( "REASON 7: segment addition postulate<BR>\n" );
document.write( "STATEMENT 8: ye + ex = pq ; pe + eq = xy<BR>\n" );
document.write( "REASON 8: substitution [6,7]<BR>\n" );
document.write( "STATEMENT 9: pq = xy<BR>\n" );
document.write( "REASON 9: substitution [7,8]\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );