# Where does the square intersect with the circle?

A circle is drawn with center at origin, O, and radius $$6$$ cm. Find the coordinates of all intersections of the circle with an origin centered square of side length $$10$$ cm whose sides are parallel to the coordinate axes as illustrated in Figure 1.

I have tried this question by setting the formula for this circle $$(x^2+y^2=6)$$ into the lines $$y=5$$ and $$x=5$$, since the length of each side of the square is $$10$$cm and it is symmetrical about the origin and therefore, each side is an equal distance from the origin which is half the length of each side. However, I got imaginary numbers.

• The equation of the circle is $x^2+y^2=36$. – David Mitra Apr 17 at 11:01
• Actually you need only one intersection with one line (find the other intersection points using symmetry). For instance, the intersection with the line $x=5$ yields $y^2=36-25=11$, so $y=\pm\sqrt{11}$. You have then the points $(\pm5,\pm\sqrt{11})$ and $(\pm\sqrt{11},\pm5)$, with any combination of signs (hence $8$ points). – Jean-Claude Arbaut Apr 17 at 11:04