Respuesta :
The area of a circle is given by
[tex] A = \pi r^2 [/tex]
whereas the circumference is given by
[tex] C = 2\pi r [/tex]
If we want these two values to be (numerically) the same we have to set [tex] A=C [/tex] and solve for the radius:
[tex] A = C \iff \pi r^2 = 2\pi r \iff r^2 = 2r \iff r^2-2r=0 \iff r(r-2) = 0[/tex]
So, one (trivial) solution is [tex] r=0 [/tex]. A circle with radius 0 is just a point, and so both area and circumference are zero.
The other solution is [tex] r = 2 [/tex]. In fact, you have
[tex] A = \pi r^2 = 4\pi,\quad C = 2\pi r = 2\pi \cdot 2 = 4\pi [/tex]
