CBSE Class 12-science Answered

The given line x+y=52, has a slope of -1. It makes an angle 45 with x axis, on the given circle side.

Draw a perpendicular to this line from origin, and what we get is a right angled triangle, whose hypotenuse is the 52.

The perpendicular distance from the origin i.e. centre of the given circle onto the line, x+y = 52,

is, 52 sin45 = 5 and it's a line with slope 1, since it's perpendicular to the line of slope -1.

But this perpendicular distance will be,

Radius of the given circle + Diameter of the smallest circle required,

2 + d = 5

d = 3

And the smaller circle lies on this line, i.e. y = x,

The distance of the centre of smaller circle from origin, is 2+1.5 = 3.5.

Hence it's x coordinate, 3.5 sin 45 = 72/4.

Therefore, the coordinates of the smaller circle, (72/4, 72/4).

Regards,

Team,

TopperLearning.