Two circles support a triangle. Prove it is equilateral.

Scroll down for a solution to this problem.

## Solution

The proof follows these steps:

- Because AB is a radius of both circles, they are congruent.
- Inspection of the sides of triangles ABC and ABF reveals they are both equilateral.
- The angle at the centre FAC is therefore 120°.
- Using the Inscribed angle theorem, it follows that angle FDC is 60°.
- Similarly angle FEC is 60°.
- Using the interior angle sum, also angle DCE is 60°, so all three angles of triangle DEC are equal.

Please look here for a nice animation of this puzzle by Ignacio Larrosa Cañestro.

## Poem

Where is our place ?

In the middle of what ?

The earth in the Cosmos, in the Universe?

But we are not the center

Passing through the Milky Way

What is Universe ?

Finished or Infinite

But we know

We are in the middle of our feelings, living and dying

One day !

## Poem 2

Feeling

Balancing

Coming

And

Going

Dancing

With

Soul and

Heart

And

Spirit

A caress

With tenderness