# Tag Archives: median

## Mean and Median

What is the number of distinct real numbers that have the property that the median of the five numbers is equal to their mean? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Suppose is the smallest number. We order the five … Continue reading

## 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

## Median of a Trapezoid

The trapezoid has and . The three congruent sides have lengths . Find the length of the median in terms of . Source: NCTM Mathematics Teacher 2008 SOLUTION Triangle is a triangle with hypotenuse equal . Likewise Median of trapezoid … Continue reading

## Mean of 41

A set of seven different positive integers has a median of and a mean of . What is the greatest possible value of one of the seven positive integers? Source: mathcontest.olemiss.edu 11/18/2013 SOLUTION First guess and check Median  Mean too … Continue reading

## Three Tangent Circles

Three mutually tangent circles of radius one are surrounded by a larger circle that is simultaneously tangent to all three. What is the radius of the larger circle? Source: http://www.mathcircles.org SOLUTION The centers of the three mutually tangent circles form … Continue reading