Tag Archives: perpendicular bisector

Equilateral Triangle and Square

A pentagon made up of equilateral triangle with side length on top of square is inside a circle passing through points , and . Find the radius of the circle. Source: NCTM Mathematics Teacher, August 2006 Solution Let be the … 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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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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Inscribed Circle of Equilateral Triangle

The circumference of a circle circumscribing an equilateral triangle is units. Find the number of square units in the area of the circle inscribed in the same triangle. Source: NCTM Mathematics Teacher, February 2006 SOLUTION In equilateral triangle , angle … Continue reading

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Equal Triangles

Two different triangles have the same area but different perimeters. Triangle has side lengths of and cm. Triangle has two sides with length of cm. Find the length of the third side of triangle . Round your answer to the nearest … Continue reading

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Triangle ADE

Points A, B, C, and D are all on segment AD, in the order listed. Segment AB is congruent to segment CD. Segment BC equals 12 units in length. Also, an additional point E exists that is not on segment … Continue reading

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Inscribed in a Circle

An equilateral triangle and regular hexagon are inscribed in the same circle.   Find the ratio of the area of the triangle to that of the hexagon. Source: mathcontest.olemiss.edu 12/7/2009 SOLUTION First, rotate the equilateral triangle around center of the circle … Continue reading

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