Radius please

Geometry Level 2

The smaller circle touches the bigger circle and also its perpendicular diameters. If the radius of the smaller circle is 2 cm, find the radius of the bigger circle.

The answer is 4.828.

1 solution

Nishant Ranjan
Nov 18, 2019

Let us focus on only the quadrant containing the smaller circle.

Notice that we can make a right angled triangle O'AO with side lengths:

O'A = 2cm (radius of small circle)

AO = 2cm (obviously)

Now, use Pythagoras theorem:

$h^{2} = p^{2} + b^{2}$ $=> O'O^{2} = O'A^{2} + AO^{2}$ $=>O'O^2 = 4 + 4$ $=>O'O = 2\sqrt{2}$

Now, the required length is OP.

$OP = O'O + O'P$ $O'P = radius = 2cm$ $Thus,$ $OP = 2\sqrt{2} + 2 = \boxed{~ 4.828} (Approximately)$

I just barely got it right on my last attempt. I recently learned inversive geometry and was experimenting with this sort of circle packing thing, was going to be really mad if I didnt get it right to get opportunity to post solution to let people know that i know this kind of stuff

chase marangu - 1 year, 3 months ago

Radius please

The answer is 4.828.

1 solution

0 pending reports