### All GMAT Math Resources

## Example Questions

### Example Question #61 : Geometry

The points and form a line which passes through the center of circle Q. Both points are on circle Q.

To the nearest hundreth, what is the length of the radius of circle Q?

**Possible Answers:**

**Correct answer:**

To begin this problem, we need to recognize that the distance between points L and K is our diameter. Segment LK passes from one point on circle Q through the center, to another point on circle Q. Sounds like a diameter to me! Use distance formula to find the length of LK.

Plug in our points and simplify:

Now, don't be fooled into choosing 13.15. That is our diameter, so our radius will be half of 13.15, or 6.575. This rounds to 6.58

### Example Question #62 : Geometry

If the trunk of a particular tree is feet around at chest height, what is the radius of the tree at the same height?

**Possible Answers:**

**Correct answer:**

A close reading of the question reveals that we are given the circumference and asked to find the radius.

Circumference formula:

So,

So 17 feet

### Example Question #63 : Geometry

If the circumference of a circle is , what is its radius?

**Possible Answers:**

**Correct answer:**

Using the formula for the circumference of a circle, we can solve for its radius. Plugging in the given value for the circumference, we have:

### Example Question #1 : Calculating The Length Of A Radius

If the area of a circle is , what is its radius?

**Possible Answers:**

**Correct answer:**

Using the formula for the area of a circle, we can solve for its radius. Plugging in the given value for the area of the circle, we have:

### Example Question #65 : Geometry

Given that the area of a circle is , determine the radius.

**Possible Answers:**

**Correct answer:**

To solve, use the formula for the area of a circle, , and solve for .

### Example Question #2 : Calculating The Length Of A Radius

Given a circumferene of , find the circle's radius.

**Possible Answers:**

**Correct answer:**

The circumference of a circle, in terms of radius, can be found by:

We are told the circumference with respect to so we can easily solve for the radius:

Notice how the cancels out

### Example Question #67 : Geometry

The circumference of a circle measures . Find the radius.

**Possible Answers:**

**Correct answer:**

Solving this problem is rather straightforward, we just need to remember the circumference of circle is found by and in this case, we're given the circumference in terms of .

Notice how the cancel out

### Example Question #68 : Geometry

The arc of a circle measures . The chord of the arc, , has length . Give the length of the radius of the circle.

**Possible Answers:**

**Correct answer:**

A circle can be divided into three congruent arcs that measure

.

If the three (congruent) chords are constructed, the figure will be an equilateral triangle. The figure is below, along with the altitudes of the triangle:

Since , it follows by way of the 30-60-90 Triangle Theorem that

and

The three altitudes of an equilateral triangle split each other into segments that have ratio 2:1. Therefore,

### Example Question #11 : Calculating The Length Of A Radius

The arc of a circle measures . The chord of the arc, , has length . Give the radius of the circle.

**Possible Answers:**

**Correct answer:**

A circle can be divided into four congruent arcs that measure

.

If the four (congruent) chords of the arcs are constructed, they will form a square with sides of length . The diagonal of a square has length times that of a side, which will be

A diagonal of the square is also a diameter of the circle; the circle will have radius half this length, or

### Example Question #11 : Calculating The Length Of A Radius

Two circles in the same plane have the same center. The larger circle has radius 10; the area of the region between the circles is . What is the radius of the smaller circle?

**Possible Answers:**

**Correct answer:**

The area of a circle with radius is .

Let be the radius of the smaller circle. Its area is . The area of the larger circle is . Since the area of the region between the circles is , and is the difference of these areas, we have

The smaller circle has radius .

Certified Tutor

Certified Tutor