# GRE Math : How to find the length of a radius

## Example Questions

### Example Question #11 : Radius

"O" is the center of the circle as shown below.

A

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B

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3

Quanitity A is greater

Quantity B is greater

The relationship cannot be determined

The two quantities are equal

Quantity B is greater

Explanation:

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 + a= c2 → 2r= 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)

Explanation:

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)≠ 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  feet. What is the radius of this fence?

Explanation:

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  feet, so we can say:

Solving for , we get:

Some students may be intimidated by having  in the denominator; however, there is no need for such intimidation. This is simply the answer!

### Example Question #2 : How To Find The Length Of A Radius

Circle  has a center in the center of Square .

The area of Square ABCD is  .

What is the radius of Circle ?