First I'm going to go through the choices with you and evaluate
each one. Then after that, I'm going to hand you a secret that
I promise is going to knock your socks off.
a- Calculate the ratio of the diameter to the radius for each circle
and show that they are equal.
-- That won't tell you anything. The ratio of the diameter
to the radius of EVERY circle is 2 .
b- Calculate the ratio of degrees to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The circumference
of EVERY circle subtends a central angle of 360°.
c- Calculate the ratio of the área to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The ratio of the area
to the circumference of EVERY circle is (radius/2).
They're only equal if the circles are the same size.
d- Calculate the ratio of the diameter to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The ratio of the diameter
to the circumference of EVERY circle is 1/pi. If the ratio isn't
1/pi, then you're not looking at a circle.
None of these choices tells you whether the two circles are similar.
What are you going to do ? How can you tell ? ?
Here's the surprise I promised you.
Beware of flying socks:
All circles are similar to all other circles.
Good night.