BrainDen.com - Brain Teasers
• 0

# Three Big Wheels

## Question

How much of the area of a 3 4 5 right triangle can be covered

by three non overlapping circles completely contained by the triangle?

• 1
• 1

## Recommended Posts

• 0

74.13% if biggest r =1 medium r = 0.5195 big r = 0.382

##### Share on other sites

• 0

How much of the area of a 3 4 5 right triangle can be covered

by three non overlapping circles completely contained by the triangle?

60%

##### Share on other sites

• 0

73.09% if biggest r =1

##### Share on other sites

• 0

77%

.53 =r1

1.01=r2

.41=r3

looks like i am approaching 80%

##### Share on other sites

• 0

I programmed the Malfatti circles for this problem.

They give 66.27% coverage, thought initially to be optimal, clearly not.

##### Share on other sites

• 0

I programmed the Malfatti circles for this problem.

They give 66.27% coverage, thought initially to be optimal, clearly not.

but 1.01 for r1 is stepping on the line..the limit is 1

##### Share on other sites

• 0

I programmed the Malfatti circles for this problem.

They give 66.27% coverage, thought initially to be optimal, clearly not.

but 1.01 for r1 is stepping on the line..the limit is 1

The incircle has radius of 1. Good catch ...

The competition is still open.

I'll mark it solved at 74.13 until/unless a better number comes in.

• 0

darn

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.