User:5849206328x: Difference between revisions

Revision as of 18:48, 2 July 2014

$[asy] // scale the image unitsize(126); pair A, B, L, P, T; A = dir(195); L = dir(270); B = dir(345); dot(A); dot(B); dot(L); draw(A--B); draw(circumcircle(A,B,L)); P = (2*A + B)/3; dot(P); T = intersectionpoints(circumcircle(A,B,L),L--(L + 100*(P - L)))[0]; dot(T); draw(circumcircle(T,P,P+(0.0000001,0))); draw(L--T); label("$A$",A,NE); label("$B$",B,NE); label("$L$",L,NE); label("$P$",P,NE); label("$T$",T,NNW); [/asy]$

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User:5849206328x: Difference between revisions

Revision as of 18:48, 2 July 2014

@@ Line 1: / Line 1: @@
 <asy>
 // scale the image
-unitsize(108);
+unitsize(126);
-pair A, B, C, I, L, Ia;
+pair A, B, L, P, T;
-A = dir(111); B = dir(207); C = dir(333); dot(A); dot(B); dot(C);
+A = dir(195); L = dir(270); B = dir(345); dot(A); dot(B); dot(L);
-draw(A--B--C--cycle);
+draw(A--B);
-draw(circumcircle(A,B,C));
+draw(circumcircle(A,B,L));
-I = incenter(A,B,C); dot(I);
+P = (2*A + B)/3; dot(P);
-draw(circumcircle(B,I,C),dashed);
+T = intersectionpoints(circumcircle(A,B,L),L--(L + 100*(P - L)))[0]; dot(T);
-L = intersectionpoints(circumcircle(A,B,C),A--(A + 100 * (I - A)))[1]; dot(L);
+draw(circumcircle(T,P,P+(0.0000001,0)));
-Ia = intersectionpoints(circumcircle(B,I,C),A--(A + 100 * (I - A)))[1]; dot(Ia);
+draw(L--T);
-draw(A--Ia);
 label("$A$",A,NE);
-label("$B$",B,WNW);
+label("$B$",B,NE);
-label("$C$",C,ENE);
-label("$I$",I,NE);
 label("$L$",L,NE);
-label("$I_a$",Ia,NNE);
+label("$P$",P,NE);
+label("$T$",T,NNW);
 </asy>