Lines - SSAT Middle Level: Quantitative

The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches.

By the Segment Addition Postulate,

By the Segment Addition Postulate,

The length of a line segment can be determined using the distance formula:

To find the length of this line, you can subtract to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

We can use the distance formula:

The radius is the distance from the center of the circle to anypoint on the circle. So we can use the distance formula in order to find the radius of the circle:

A rectangle has two diagonals with the same length. So we should find the length of . We can use the distance formula:

In geometry, a right angle triangle can occur with the ratio of in which 3 and 4 are each leg lengths, and 5 is the hypotenuse.

When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.

Here, the ratio is:

This is double the ratio. Therefore, we should multiply 4 by 2 in order to solve for the missing leg, which would be a value of 8 feet.

Another way to solve is to use the Pythagorean Theorem: .

We know that one leg is 6 feet and the hypotenuse is 10 feet.

By definition, the radius and diameter of a circle are related by the following equation:

Plugging in as stated in the question, we find that .

Since the question is asking us for the value of :

.

Since we are dealing with a right triangle, we can use the Pythagorean Theorem:

,

where and are leg lengths of and , respectively, and is the length of the hypotenuse.

Substituting values into the Theorem:

A line that is bisected is split into two segments of equal length. Therefore, if line is bisected at point ,

.

Consequently, bisecting line segment at point :

If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.

The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches.

By the Segment Addition Postulate,

By the Segment Addition Postulate,

The length of a line segment can be determined using the distance formula:

To find the length of this line, you can subtract to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

We can use the distance formula: