# Did i just make a new formula?

I was drawing two tangent circle many as I could with integer radius. I notice there is some pattern, so i quickly observe and find out 4 formula for two tangent circle.

Assume that $$AC$$ and $$AD$$ is $$R$$ , and $$BF$$ and $$BE$$ is $$r$$. Now these are the formula that i have founded,

1. $$\Large AP = \frac{R}{R + r} \times AB$$

2. $$\Large PB = \frac{r}{R+r} \times AB$$

3. $$\Large BQ = \frac{r}{R-r} \times AB$$

4. $$\Large AQ = \frac{R}{R-r} \times AB$$

Now to my question,

1. Why did this formula work? I just analysis a pattern.

2. Have you guys ever heard of this formula before?

Note by Jason Chrysoprase
2 years 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:

Triangles ADP and BFP are similar with ratio $$R : r$$. Triangles ACQ and BEQ are similar with ratio $$R : r$$. So $$AP : AB = AP : (AP + PB) = R : (R + r)$$ by the similarity, and likewise with the rest.

- 2 years ago

Similarity of triangles must be used here as Ivan sir suggested, btw nice observation jason.!

- 2 years ago

Ohhh, i get it

- 2 years ago