A geometry problem by Rishabh Tiwari

Geometry Level 5

Find the length of the side of smallest equilateral triangle in which three disks of radii 2, 3, and 4 can be placed without overlap?

If the answer is of the form $b\sqrt{c}$ , where $b$ , and $c$ are positive integers and $c$ is square-free. Find $b + c$ .

1 solution

Niranjan Khanderia
Jun 7, 2016

$11\sqrt3=a\sqrt b.\ \ \ \therefore\ a+b=11+3=14.$

I think you mistook the angle in the blue & yellow triangles, it should be $30^\circ$ instead of $60^\circ$ , btw perfect solution $+1!$

Rishabh Tiwari - 5 years ago

Thank you. I have corrected...

Niranjan Khanderia - 5 years ago

Shouldn't the angle be 30 degrees?? You say that you have corrected it, but it still shows the same. btw, awesome solution!!

Pranav Saxena - 4 years, 10 months ago

You are correct. I did correct it only at that time. But forgot to transmit to Brilliant. Sorry for that.

Niranjan Khanderia - 4 years, 10 months ago