GRE Math : How to find the length of a radius
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Example Question #11 : Geometry
"O" is the center of the circle as shown below.
A
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The radius of the circle
B
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3
The relationship cannot be determined
Quantity B is greater
The two quantities are equal
Quanitity A is greater
Quantity B is greater
We know the triangle inscribed within the circle must be isosceles, as it contains a 90-degree angle and fixed radii. As such, the opposite angles must be equal. Therefore we can use a simplified version of the Pythagorean Theorem,
a2 + a2 = c2 → 2r2 = 16 → r2 = 8; r = √8 < 3. (since we know √9 = 3, we know √8 must be less); therefore, Quantity B is greater.
Example Question #11 : Geometry
Which point could lie on the circle with radius 5 and center (1,2)?
(4,6)
(3,–2)
(–3, 6)
(4,–1)
(3,4)
(4,6)
A radius of 5 means we need a distance of 5 from the center to any points on the circle. We need 52 = (1 – x2)2 + (2 – y2)2. Let's start with the first point, (3,4). (1 – 3)2 + (2 – 4)2 ≠ 25. Next let's try (4,6). (1 – 4)2 + (2 – 6)2 = 25, so (4,6) is our answer. The same can be done for the other three points to prove they are incorrect answers, but this is something to do ONLY if you have enough time.
Example Question #1 : How To Find The Length Of A Radius
A circular fence around a monument has a circumference of 
This question is easy on the whole, though you must not be intimidated by one small fact that we will soon see. Set up your standard circumference equation:
The circumference is 
Solving for 
Some students may be intimidated by having 
Example Question #2 : How To Find The Length Of A Radius
Circle 
The area of Square ABCD is 
What is the radius of Circle 
Since we know that the area of Square 
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