Which of the following could be both within a square with radius of 1?

A square cannot have a radius, it can only have a side and a diagonal.

Assuming the question means to say, that the " Radius of a circle inscribed in a square is 1 cms " then which of the following two points could be within the square?

If the radius of the inscribed circle is \(1\) cms then the square is of side \(2\) cms and the longest distance within the square is \(2\sqrt{2}\). So the distance within the two points should be less than \(2\sqrt{2}\) to fulfill the criteria.

IF the distance between the two points is more than \(2\sqrt{2}\) then both the points cannot be inside the square.

(A) (1,1) and (2,3) -> \(\sqrt{5} > 2\sqrt{2}\)

(B) (-2,-1) and (1, 2) ->\(3\sqrt{2}> 2\sqrt{2}\)

(C) (4, 6) and (5, 5) -> \(\sqrt{2} < 2\sqrt{2}\)

(D) (-5,-6) and (-7, -8) -> \(2\sqrt{2} = 2\sqrt{2}\)

(E) (-3,0) and (0,-4) -> \(5 > 2\sqrt{2}\)

Since we are asked within the square , choice C is the best option.



Ans C

Hope it's clear.