User:Jonjoseph

$[asy] pair O = (0,0); pair P = (2,0); draw(unitcircle); dot(O); dot(P); label('$P$', P, E); label('$C$', O, W); [/asy]$

Given a circle with center $C$ and a point $P$ that lies outside the circle, bisect circle $C$ with a second circle centered at $P$ .

$[asy] pair O = (0,0); pair P = (2,0); pair A = (0,1); pair B = (0, -1); draw(unitcircle); draw(A--B, red); draw(P--O, red); draw(circle(P, 2.24)); dot(O); dot(P); dot(A); dot(B); label('$P$', P, E); label('$C$', O, W); [/asy]$

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$",V,NE); draw(X--Y); draw(Z--Y, dashed); draw(W--X, red); draw(X--Z, red); draw(Z--U, red); draw(Z--W,red); draw(U--X, red); draw(S--T--U--V--cycle); draw(X--T); draw(W--S); draw(Y--U); draw(Z--V,dashed); draw(W--U,red); [/asy]$

$[asy] unitsize(0.2 cm); pair A, B, E, P; A = (0,0); B = (8,0); E=(1,2); P = (B + reflect(A,(1,2))*(B))/2; draw((-10,0)--(10,0)); draw(A+(-1,-2)--8*E, red); draw(A--(0,25)); draw(B+-1*(1,2)--(9, 2)+7*(1,2), red); draw(B--P,dashed); dot("$A$", A, SE); dot("$B$", B, SE); dot("$P$", P, N); label("$8$", (A + B)/2, S); [/asy]$

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User:Jonjoseph