Tag Archives: circle

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

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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

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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

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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

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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

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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

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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

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Square in Circle

A square of maximum area is inscribed in a semicircle as shown. What percent of the area of the circle is outside the square? Source: NCTM Mathematics Teacher, January 2006 SOLUTION area of circle = area of square = area … Continue reading

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Points on Circle

Find all points that have an -coordinate twice the -coordinate and that lie on a circle of radius with center at . Source: NCTM Mathematics Teacher, January 2006 SOLUTION Let for some real number . Equation of circle or or … Continue reading

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Circles Within Square

The two circles in the figure are congruent and have their centers on the line . They are tangent to each other and to the square . The radius of the circles is . Calculate the area of the square … Continue reading

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