Two circles support a triangle. Prove it is equilateral.
Scroll down for a solution to this problem.
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.
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 !