Tag Archives: circumcircle

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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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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Area of Triangle

Without using Heron’s formula, find the area of the triangle. Source: NCTM Mathematics Teacher, January 2006 SOLUTION Applying the Law of Cosines Area of triangle Answer: square units Alternative solution 1 Most textbooks state the Law of Sines as We have … 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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Pesky Aliens

A Duram wheat farmer making his living in Edmonton, Alberta, Canada awoke one morning to find a huge crop circle in the middle of his largest field. While preparing the insurance claims paperwork, aerial photos revealed two overlaid equilateral triangles … Continue reading

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Intersecting Circumcircles

The given in the above figure are: is a right triangle at is a right triangle at Points , and are collinear Points , and are collinear cm cm 1. (a) What is the measure of ? (b) Deduce from … Continue reading

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Isosceles Triangle Inscribed In a Circle

is an isosceles triangle with a vertex at  such that . is the circumcircle of triangle ; is the center of circle ; is a diameter of . 1. What kind of triangle is triangle ? Justify your answer. 2. (a) … 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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