# Tag Archives: circle

## Rolling Wheel

If a wheel completes exactly revolutions while rolling feet, what is the diameter of the wheel? Source: NCTN Mathematics Teacher, September 2006 Solution The above figure shows the ground distance traveled by the rolling wheel of radius feet in revolutions. … Continue reading

## Area of a Disc

If the area of a disc inscribed in a square is square centimeters, what is the area of the square? Source: NCTM Mathematics Teacher, September 2006 Solution Area of disc = Area of square = Answer: square centimeters

## Real Solutions (x,y)

How many real solutions are there that satisfy the two equations and ? Source: NCTM Mathematics Teacher, September 2006 Solution The graph of is a circle centered at the origin and radius = . The graph of is a hyperbola … Continue reading

## Arc of a Circle

is a diameter of a circle of radius unit. is a chord perpendicular to that cuts at . If the arc is of the circumference of the circle, what is the length of the segment ? Source: NCTM Mathematics Teacher, … Continue reading

## Biggest Pizza Slice

An 8-inch pizza is cut into equal slices. A 10-inch pizza is cut into equal slices. A 12-inch pizza is cut into equal slices. A 14-inch pizza is cut into equal slices. From which pizza would you take a slice … Continue reading

## Tangent Lines

Suppose to co-planar circles and have no points in common. Determine how many lines, if any, are tangent to both and ? Source: NCTM Mathematics Teacher, October 2006 Solution When one circle is inside the other, there are no tangent … Continue reading

## Three Intersecting Circles

Circle has a radius of and its center is at . Circle has a radius of and its center at . What is the length of the radius of a third circle (Circle ) that passes through the center of … Continue reading

## Lattice Points

A point with integral coordinates is called a lattice point. For example, is a lattice point, whereas is not. How many lattice points lie on the graph of ? Source: NCTM Mathematics Teacher, January 2006 Solution The graph of is … Continue reading

## Circular Garden

Ebru’s backyard is a square with side length of meters. Her backyard has a circular garden that extends to each side of the yard. In the center of the garden is a square patch of asparagus so big that each … Continue reading

## Points in a Plane

Find all points in a plane that are cm from a given segment cm long and are also cm from the midpoint of the segment. Source: NCTM Mathematics Teacher, January 2006 SOLUTION Segments and are parallel to the given segment … Continue reading