In some SAT circle problems you cannot have even an idea from math diagram of how to solve the circle problems. It means that the information given in the math shape is not sufficient. In such case, drawing an additional line by your judgment may help you to solve math circle problems. Following is an example to illustrate you how an additional line is added to solve circle problems in geometry.
How to solve circle problems:Example
In the figure, C is a point on the circle whose centre is O and whose radius is r, and OACB is a rectangle. What is the length of diagonal?
(A) 2/3 r
(B) r
(C) r2
(D) r2/2 п
(E) 2 r2/ п
Solution:
It is difficult to have an idea of diagonal AB with information given in the figure. So we draw line of radius OC (dotted line). 
We observe that OC and AB are diagonals of rectangle OABC. Since diagonal of a rectangle are always equal, so diagonal AB is equal to diagonal OC, which is radius r (B).
See you need not to use circle formula or triangle formula or Pythagorean Theorem to calculate the radius of the circle in this circle problem.
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How to solve circle problems easily?
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This is another approach to solving circle geometry questions. great idea!