Intersection of Line and Circle

Hard Geometry Circles

Consider a circle centered at the origin with the equation $$x^2 + y^2 = r^2$$, where $$r$$ is the radius of the circle. A line passes through the point (r, 0) and makes an angle of $$30^ ext{o}$$ with the positive x-axis. Determine the coordinates where this line intersects the circle.

What are the coordinates of the intersection points of the line with the circle?

($$r, 0$$) and ($$\frac{r}{2}, \frac{r\sqrt{3}}{2}$$)

($$0, r$$) and ($$\frac{r}{2}, \frac{r\sqrt{3}}{2}$$)

($$r, 0$$) and ($$r, \frac{r\sqrt{3}}{3}$$)

($$r, 0$$) and ($$\frac{r}{2}, \frac{r}{2}$$)

Hint

Submitted3.4K

Correct3.0K

% Correct89%