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Okay,my exams have ended,as n tends to infinity the bases will become infinitesimal,it can be proved using law of cosines.and as the n tends to infinity angle will become small and arc will become small,so both arc and base will become equal and it follows that area will be equal
my textbook uses the fact that as n tends to infinity sum of the triangles' base equals to circumference.I'd love to prove it but i'm busy cause my exams have started...
I discovered another proof,the angle standing on a diameter is right,so the angles standing on both side of diameter are right and equal.and equal angles in a circle are stand on similar amd equal arc (congruent arcs).so,the arcs on both side of diameters are equal and it follows the sides are equal in area.
Hm, can you prove that it will tend to the area as n goes to infinity.
Sorry,i didn't find it in the net,i kinda discovered it.
That is still not clear. Could you give a link?
(sorry,can't post pics,somethings wrong with my browser and my english is also shaky)
Please post the proof
Never mind,i've found a proof.
The second part doesn't actually follow directly from the first so I guess a proof is still needed. I'll give it some thought.
Define a diameter
This proof isn't actually needed by me,but i am curious how to prove it,"the diameter of a circle divides the circle into 2 equal parts"