Three tangent circles inside a larger circle Suppose you're given a circle with center $O$, I'm curious, how can one construct with ruler and compass three circles inside the larger circle such that each is tangent to the larger circle as well as to the other two?
 A: 
In the image above are sequential steps of how I did it (left image is the earlier steps and the right the later steps). I'll only explain the figure constructed in the center. After having divided the disk into three (left figure) by the three radius, construct an arbitrary chord S perpendicular to AB. Construct circle centered at T tangent to the given circle at U. Construct a line passing U and the point at which the perpendicular and the the circle centered at T intersects. The line should intersect at diameter AB which is the tangent. The rest is easier to follow from the figure. 
I was looking for the answer for this problem in the net but to no avail. After much trial and error, got this construction. Not 100% sure though, kinda new to this non-coordinate based geometry. 
A: If the radius of the circle is 1, the radius of three circles that will be internally tangent is $2\sqrt{3}-3\approx 0.464$ by Soddy's formula, given in the Soddy's circles section of this.  You can construct this length, then mark it off on a diameter of the circle to find one of the centers, and finish constructing the equilateral triangle.
Added:  For the construction, make a right angle with 1 on one side, swing 2 as a hypotenuse, and you have $\sqrt{3}$.  Then you can mark a line to get $2\sqrt{3}-3$.  Draw a diameter of the circle you are given and mark off $2\sqrt{3}-3$ from the circumfrence to find the center of one circle.  Construct an equilateral triangle of $2(2\sqrt{3}-3)$ bisected by the diameter and you have the three centers.
