×

Circles and Circles

Let Circle A be external tangent to Circle B. Let Circle C be external tangent to both Circle A and B. All three circles are external tangent to a line. Prove that for any given radius of Circle A and B, for example, x and y, respectively, the radius of the Circle C with radius z can be expressed as [1/sqrt(x)]+[1/sqrt(y)]= [1/sqrt(z)]

Note by Raymond Park
1 year, 8 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

- 1 year, 8 months ago

Any other way?

- 1 year, 8 months ago

Here's another way.

We first prove the following lemma:

Using this lemma, we get the following proof:

- 1 year, 8 months ago

- 1 year, 8 months ago

Well done!

- 1 year, 8 months ago