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if O is the center of the circle and P is on its circumference, then OP is a radius
Because of one of the Circle Theorems that states that the angle subtended by any arc at the centre of the circle is half that at the circumference. A rough version of the proof follows: Suppose the quadrilateral ABCD is inscribed in a circle with centre O. Join AO and CO. This partitions the circumference into two arcs - both AC but going around different sides of the centre. One of the arcs AC, subtends angle B at the circumference and suppose the angle subtended by the same arc at O is X. Then 2B = X The other arc AC subtends angle D at the circumference and suppose the angle subtended by the same arc at O is Y. Then 2D = Y So 2B + 2D = X + Y But X + Y = 360 degrees. So B + D = 180 that is, B and D are supplementary. And then, since A+B+C+D = 360, A + C = 180. The converse can be proved similarly.
Join the centre of the circle O and the point A .Extend it to both sides to form a line.This is the required locus
all the points in the inscribed circle are also in the bigger circle. If all the points in the outside circle are the set O ... and all the points in the inner circle are the set I... Then I is a subset of O, just like a venn diagram
the number is spelled pi, not pie. Pie is a food, pi is different.Pi is an irrational number (number which doesn't end) which is the ratio to the circumference o f a circle to its diameter.Some beginning numbers of pi are: 3.14159265358979323846264338327950288419716939937510...and so on