If $c >0$, $c≠ 1$, $z_1≠z_2$, prove that $\frac{|z-z_1 |}{|z-z_2 | }=c$ represents a circle. Find its center and radius.
122060
Apollonius circle, its radius and center
77470
Find modulus of $\frac{|z_1-z_2|}{|1-(z_1)(\overline{z_2})|}$
84189
Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
73892
Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$
65923
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
110103
Prove that there are $0<c_1 < c_2<1$ s.t. $\frac{1}{g'(c_1)}+\frac{1}{g'(c_2)}=2$ . The same for $g'(c_1)g'(c_2)=1$.
145509
Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
39492
Finding $z\in \mathbb C$ with $\sin z = 2$?
44562
If $\left|z+\frac{2}{z}\right |=2$, then prove that max value of $|z|$ is $\sqrt 3 + 1$ (Corrected version)
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
149319
Möbius transformations and concentric circles
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
77250
Find the linear fractional transformation that maps the circles |z-1/4| = 1/4 and |z|=1 onto two concentric circles centered at w=0?
73867
Radius of circumscribed circle of triangle as function of the sides
11338
How to find the circumcenter of a triangle and the length of the corresponding radius of the circle in $\mathbb{R}^3$
143967
Finding an equation for a circle given its center and a point through which it passes
118507
Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$