Difference between revisions of "User:Jonjoseph"
| Line 67: | Line 67: | ||
draw(Z--V,dashed); | draw(Z--V,dashed); | ||
draw(W--U,red); | draw(W--U,red); | ||
| + | </asy> | ||
| + | |||
| + | |||
| + | <asy> | ||
| + | unitsize(0.2 cm); | ||
| + | pair A, B, E, P; | ||
| + | A = (0,0); | ||
| + | B = (8,0); | ||
| + | E=(1,2); | ||
| + | P = (B + reflect(A,(1,2))*(B))/2; | ||
| + | draw((-10,0)--(10,0)); | ||
| + | draw(A+(-1,-2)--8*E, red); | ||
| + | draw(A--(0,25)); | ||
| + | draw(B+-1*(1,2)--(9, 2)+7*(1,2), red); | ||
| + | draw(B--P,dashed); | ||
| + | dot("$A$", A, SE); | ||
| + | dot("$B$", B, SE); | ||
| + | dot("$P$", P, N); | ||
| + | label("$8$", (A + B)/2, S); | ||
</asy> | </asy> | ||
Revision as of 20:29, 26 March 2014
![[asy] pair O = (0,0); pair P = (2,0); draw(unitcircle); dot(O); dot(P); label('$P$', P, E); label('$C$', O, W); [/asy]](http://latex.artofproblemsolving.com/f/8/c/f8c42e0581ece077163a0525688493127ba20734.png)
Given a circle with center 
and a point 
that lies outside the circle, bisect circle with a second circle centered at .
![[asy] pair O = (0,0); pair P = (2,0); pair A = (0,1); pair B = (0, -1); draw(unitcircle); draw(A--B, red); draw(P--O, red); draw(circle(P, 2.24)); dot(O); dot(P); dot(A); dot(B); label('$P$', P, E); label('$C$', O, W); [/asy]](http://latex.artofproblemsolving.com/e/b/4/eb4535e9b70c84a691a32b89d485892fe6de6140.png)
Problem from class:
![[asy] import olympiad; import cse5; import geometry; size(150); defaultpen(fontsize(10pt)); defaultpen(0.8); dotfactor=4; pair X = origin; pair Y = (3,0); pair W = X+dir(120); pair Z = Y+dir(120); pair T = (0,2); pair S = T+dir(120); pair U = (3,2); pair V = U+dir(120); label("$X$",X,SW); label("$W$",W,SW); label("$T$",T,NE); label("$S$",S,NW); label("$Z$",Z,E); label("$Y$",Y,SE); label("$U$",U,E); label("$V$",V,NE); draw(X--Y); draw(Z--Y, dashed); draw(W--X, red); draw(X--Z, red); draw(Z--U, red); draw(Z--W,red); draw(U--X, red); draw(S--T--U--V--cycle); draw(X--T); draw(W--S); draw(Y--U); draw(Z--V,dashed); draw(W--U,red); [/asy]](http://latex.artofproblemsolving.com/d/3/d/d3da50bbda0e54e8877f454374bdab7022ed1881.png)
![[asy] unitsize(0.2 cm); pair A, B, E, P; A = (0,0); B = (8,0); E=(1,2); P = (B + reflect(A,(1,2))*(B))/2; draw((-10,0)--(10,0)); draw(A+(-1,-2)--8*E, red); draw(A--(0,25)); draw(B+-1*(1,2)--(9, 2)+7*(1,2), red); draw(B--P,dashed); dot("$A$", A, SE); dot("$B$", B, SE); dot("$P$", P, N); label("$8$", (A + B)/2, S); [/asy]](http://latex.artofproblemsolving.com/d/2/0/d20de7cc152e261b3e6ac322e36b265c71fa8902.png)
