Notes
two circles in an equilateral triangle solution

Solution to the Two Circles in an Equilateral Triangle Puzzle

Two Circles in an Equilateral Triangle

What’s the side length of this equilateral triangle? Both circles have area $3$ .

Solution by Lengths in an Equilateral Triangle

Two circles in an equilateral triangle annotated

With the points labelled as above, triangle $A E B$ is half of an equilateral triangle so the length of $A E$ is twice that of $E B$ . This means that the length of $A D$ is five times the radius of one of the circles, which is $\sqrt{3}$ . The height of an equilateral triangle is $\frac{\sqrt{3}}{2}$ times the length of one of its sides, so the side of the outer equilateral triangle is:

\frac{2}{\sqrt{3}} \times 5 \sqrt{3} = 10

Created on May 28, 2025 20:35:31 by Andrew Stacey

Notes two circles in an equilateral triangle solution

Solution to the Two Circles in an Equilateral Triangle Puzzle

Solution by Lengths in an Equilateral Triangle

Notes
two circles in an equilateral triangle solution