GRE Math : How to find the length of a radius

Example Questions

Example Question #11 : Geometry

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

A

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B

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3

The relationship cannot be determined

Quanitity A is greater

The two quantities are equal

Quantity B is greater

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 : Circles

Which point could lie on the circle with radius 5 and center (1,2)?

(–3, 6)

(4,–1)

(4,6)

(3,–2)

(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 #21 : Geometry

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 #1 : 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 ?