Question

How do I prove that a circumscribed and an inscribed circle are similar using their radii?

Answer 1

I don't understand the question. All circles are similar.

Answer 2

I really don't either. The question in my assignment is this:

Let the radius of the inscribed circle be a and the radius of the circumscribed circle be b. Show that the two circles constructed (the circumscribed circle and the inscribed circle) are similar using the radius for each. You must show all work to receive credit.

Answer 3

BTW, the circles are inscribed and circumscribed in what polygon?

Answer 4

A triangle.

Answer 5

So, according to your drawing @mathstudent55, the circumsribed circle's radius is twice the inscribed radius?

Answer 6

I don't know that it's twice.

Answer 7

Ah. Well, this is a confusing question. How else are all circles similar? Obviously they're all the same basic equation, but what else is there?

Answer 8

We can try to find b in terms of a.

Answer 9

Now I see. Since the triangles are 30-60-90, the hypotenuse is twice the length of the small leg. That means you were correct, that b = 2a.