# Tag Archives: angle 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

## 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

## 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 the angle bisector of because is equidistant from and . Triangle … 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