Question 4
Two equal circles$\omega_1,\omega_2$ have centers$O_1,O_2$. Points$X,Y$ lie on segment$O_1O_2$ with$O_1Y=O_2X$. Points$A,B$ lie on$\omega_1$ and line$AB$ passes through$X$; points$C,D$ lie on$\omega_2$ and line$CD$ passes through$Y$. Prove that a circle tangent to all four lines$AO_1,BO_1,CO_2,DO_2$ exists.
The source’s assertion is preserved. Its unrestricted wording has a counterexample, explained in the editor-authored solution rather than silently adding a hypothesis.
The source’s assertion is preserved. Its unrestricted wording has a counterexample, explained in the editor-authored solution rather than silently adding a hypothesis.