Tag Archives: tangent

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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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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Big and Small Circles

Two circles of radius are tangent to each other as shown. A line is drawn tangent to both circles. A third circle is drawn so that it is tangent to both circles and the line. The radius of this smaller … Continue reading

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Product of Tangents

What is the value of the following product? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Similarly, The product of tangents equals . Answer: Alternative solution Apply the formula to our product The product of tangents equals .

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Concentric Circles

The circles in the figure are concentric. The chord is tangent to the inner circle and has length . What is the area of the non-shaded region? Source: NCTM Mathematics Teacher, November 2006 SOLUTION area of large circle = area … Continue reading

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Tangent Circles

Determine the sum of the radii of all circles that pass through the points and [at the same time] and are tangent to the -axis. Source: NCTM Mathematics Teacher, February 2006 SOLUTION Any center of the circles lie on the … Continue reading

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Three Tangent Circles

A circle is inscribed in an equilateral triangle with a side of length . Three circles are drawn externally tangent to this circle and internally tangent to two sides of the triangle. Three more circles are drawn externally tangent to … Continue reading

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Small Circle

A circle is inscribed in a sector of a circle of radius (as shown). What is the radius of the small circle? Source: NCTM Mathematics Teacher, February 2006 SOLUTION is theĀ angle bisector of because is equidistant from and . Triangle … Continue reading

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Radius of Tangent Circle

A circular arc centered at one vertex of a square of side length passes through two other vertices. A small circle is tangent to the large circle and to two sides of the square. What is the radius of the … Continue reading

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Circles Tangent to a Right Angle

In the figure, the two circles are tangent to the right angle and to one another. If the large circle has radius , what is the radius of the smaller circle? Source: NCTM Mathematics Teacher SOLUTION Let be the radius … Continue reading

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