Tag Archives: geometry

Length of Hypotenuse

Consider the line containing the points and . What is the length of the hypotenuse of the right triangle formed by the intersections of and the -and -axes? Source: NCTM Mathematics Teacher, September 2006 Solution Points , and are the … Continue reading

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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

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Ball and Cube

Suppose that the volume of a ball is equal to times the volume of a cube. What is the ratio of the surface area of the ball to that of the cube? Source: NCTM Mathematics Teacher, September 2006 Solution Let … Continue reading

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Which Triangle is Largest?

Of the following triangles given by the lengths of their sides, which one has the greatest area? (a) (b) (c) (d) (e) Source: NCTM Mathematics Teacher, September 2006 Solution Heron’s Area Formula: area = where and are the lengths of … Continue reading

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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

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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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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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Rectangle Inside a Square

An isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains. What is the length of a diagonal of the rectangle if the sum of the areas of the removed pieces … Continue reading

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Equiangular Hexagon

An equiangular hexagon with consecutive side lengths , and can be inscribed in an equilateral triangle with side length . This same equiangular hexagon can also be inscribed in a second (distinct, noncongruent) equilateral triangle with side length . What … Continue reading

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