MATHEMAGIC 20: CIRCLES

Do you want to know what's the 'Conway circle'?
Go to: http://mathworld.wolfram.com/ConwayCircle.html


The picture shows an equilateral triangle
with its inscribed and circumscribed circle.
If the area of the inscribed circle (yellow) equals pi,
than the area of the other three colored pieces also equals pi.

Can you prove it?

 

JANUS' CIRCLE THEOREM

Triangle ABC is an equilateral rectangular triangle with hypotenuse [BC].
M is the center of the inscribed circle.
Then the sum of the circumferences of the circles with diameter [AB] and [AM]
equals the circumference of the subscribed circle (with diameter [BC]).

GREEN = RED