Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is . However, the clock is reading 5:00, so there are five numbers we have to take in to account. Therefore, we multiply 30 by 5, which gives us as our answer.

First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are between each number. Since the time reads 5:00, multiply , which yields .

If two chords intersect inside a circle, both chords are cut in a way such that the products of the lengths of the two chords formed in each are the same - in other words, 

or

Therefore, .

 is a radius of the circle from the center to the point of tangency of , so 

,

and  is a right triangle. The length of leg  is known to be 24. The other leg  is a radius radius; we can find its length by dividing the circumference by :

The length hypotenuse, , can be found by applying the Pythagorean Theorem:

.

If two chords intersect inside a circle, both chords are cut in a way such that the products of the lengths of the two chords formed in each are the same - in other words, 

Solving for :

Since , it follows that , or .

If a secant segment and a tangent segment are constructed to a circle from a point outside it, the square of the distance to the circle along the tangent is equal to the product of the distances to the two points on the circle along the secant; in other words,

Simplifying, then solving for :

To compare  to 32, it suffices to compare their squares: 

, so, applying the Power of a Product Principle, then substituting,

, so

; 

it follows that

.

If a secant segment and a tangent segment are constructed to a circle from a point outside it, the square of the distance to the circle along the tangent is equal to the product of the distances to the two points on the circle intersected by the secant; in other words,

Simplifying and solving for :

Factoring out :

Either  - which is impossible, since  must be positive, or

, in which case .

If two chords intersect inside a circle, both chords are cut in a way such that the products of the lengths of the two chords formed in each are the same - in other words, 

Divide both sides of this equation by , then cancelling:

The two quantities are equal.

Let  be the radius of Circle A. Then its area is .

The area of Circle B is , so the radius of Circle B is twice that of Circle A; by a similar argument, the radius of Circle C is twice that of Circle B, or .

(a) Twice the radius of circle B is .

(b) The sum of the radii of Circles A and B is .

This makes (b) greater.

Every hour, the tip of the minute hand travels the circumference of a circle. Between noon and 1:45 PM, one and three-fourths hours pass, so the tip travels  or  times this circumference. The length of the minute hand is the radius of this circle , and the circumference of the circle is , so the distance the tip travels is  this, or

Set this equal to  feet:

 feet.

This is equivalent to 1 foot 4 inches.