00:01
In this problem, we have a small circle, which is tangent and inside of three larger identical circles of radius one, which are also tangent to each other.
00:12
And we want to find the radius of the small circle.
00:17
So for this problem, what we can do is we can draw some equilateral triangles, and we can use equality to find some angles in the triangles that we draw.
00:30
And we'll be able to fairly easily find the radius of that inner circle.
00:37
In general, for these problems, there's not really an algorithm -alorithmic approach you can take.
00:45
You really need kind of to have a little bit of experience doing these to see what you want to do to solve them.
00:53
Okay, so here's our three triangles.
00:56
So we'll just, we'll mark the center.
01:00
Of each triangle or the centers of each circle and so we're going to draw an equilateral triangle between the centers of our larger circles and then what we'll do next is from each vertices of that triangle we'll draw a segment to the center the common center of all circles here.
01:36
And so we started with this equilateral triangle with, so each one was a 60 degree angle.
01:43
Now looking at these pairs of angles here, we can say that all of these angles are 30 degrees.
01:54
And so since each of them is identical and each has that up to 60, so all of these angles are 30.
02:02
And now we can draw, so we're going to make a triangle here going from the center, right down here...