Which of the following lists the number of points at which a circle ca

oh..i did not expect tangent to be called as intersection ...

Tangent intersects the circle at exactly one point

Anyways this question is hard to get at first time... Unless you have good imagination skills... I dont thin any formula can help

Now that we know it should be simple

EvaJager has solved this here: https://gmatclub.com/forum/which-of-the ... l#p1121790

Had to use some Sc-fi imagination for this question

Think of a moving circle which can vary in size & a fixed square of constant dimensions. Now imagine the circle eclipsing the square kinda like the shadow of moon eclipsing the Sun, if you have seen images or videos of a Solar eclipse or if you are a fan of Sci fi movies like me, it will be easy to imagine. Makes me wanna watch Interstellar for the nth time.

Well back to question.

Now the moving circle is inching towards the square from outside, first touching the square at one of its corner. That is our Point 1 of intersection. Hence we are down to options D & E.

Now the circle keeps moving forward gobbling the square, intersecting two sides & still moving forward. There will come a point when the circle can touch one side tangentially & intersect two other sides each at two points. That is 5 points of intersection . Only answer choice E has 5.

Hence Answer is E.

Thanks,
GyM

Ps. You can insert Hans Zimmer's back ground score from Interstellar for added effect while moving the circle, certainly helped me.

do we have a formula to solve this instead of actually plotting the points?