Question 3
Given numbers $x\gt 0$, $y_1\gt 0$, $x_2\lt 0$, $y_2\gt 0$, $x_3\lt 0$, $y_3\lt 0$, $x_4\gt 0\gt y_4$. For each $i=1,\ldots,4$, suppose $(x_i-a)^2+(y_i-b)^2\le c^2$. Prove that $a^2+b^2\le c^2$. Express this assertion as a theorem in plane geometry.
Source note: the first symbol is printed $x\gt 0$, without subscript. The intended condition $x_1\gt 0$ is required and is explicitly adopted for the solution; the literal statement is defective.
Source note: the first symbol is printed $x\gt 0$, without subscript. The intended condition $x_1\gt 0$ is required and is explicitly adopted for the solution; the literal statement is defective.