# Tag Archives: arc

## 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

## 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

## Four Points in The Plane

We are given points and in the plane such that , whereas . Compute the measure of in degrees. Source: NCTM Mathematics Teacher SOLUTION is the center of a circle of radius passing through points . The central because is equilateral. … Continue reading

## Spot’s Doghouse

Spot’s doghouse has a regular hexagonal base that measures one yard on each side. Spot is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside the doghouse that Spot can … Continue reading

## Same Arc Length

If an arc of on circle has the same length as an arc of on circle , find the ratio of the area of circle to the area of circle . Source: NCTM Mathematics Teacher SOLUTION Let be the radius … Continue reading

## Inscribed Triangle

Prove that the total area of the regions 1 and 2 below equals the area of the triangle. Regions 3 and 4 are parts of the semi-circle in which the triangle is inscribed, and and are diameters for the other … Continue reading

## Tessellated Arcs

The tessellated figure below consists of 3 equal arcs in an equilateral triangle. Each side measures 2 inches. What is the area of the region labeled ? Source: Julia Robinson Mathematics Festival SOLUTION Draw altitude to side . Because is … Continue reading