Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

### General Information

**Number:**MAFS.912.G-C.1

**Title:**Understand and apply theorems about circles. (Geometry - Additional Cluster)

**Type:**Cluster

**Subject:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Circles

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Assessments

## Educational Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

## Tutorial

## Virtual Manipulative

## Worksheet

## Student Resources

## Original Student Tutorials

Discover how easy it is for Katie to construct an inscribed circular logo on her company's triangular pennant template. If she completes the task first, she will win a $1000 bonus! Follow along with this interactive tutorial.

Type: Original Student Tutorial

Learn the steps to circumscribe a circle around a triangle in this interactive tutorial about constructions. Grab a compass, straightedge, pencil and paper to follow along!

Type: Original Student Tutorial

## Educational Game

This interactive game helps you learn about angles and segments, lines and arcs in a circle and how they are related. You will compete against yourself and earn points as you answer questions about radius, diameter, chord, tangent line, central angles and inscribed angles and intercepted arcs.

Type: Educational Game

## Problem-Solving Tasks

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Type: Problem-Solving Task

This problem solving task challenges students to describe and compare different angles.

Type: Problem-Solving Task

This problem solving task asks students to explain certain characteristics about a triangle.

Type: Problem-Solving Task

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem.

Type: Problem-Solving Task

This problem solving task asks students to place a fire hydrant so that it is equal distance from three given points.

Type: Problem-Solving Task

This problem solving task challenges students to place a warehouse (point) an equal distance from three roads (lines).

Type: Problem-Solving Task

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle.

Type: Problem-Solving Task

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment.

Type: Problem-Solving Task

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Type: Problem-Solving Task

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Type: Problem-Solving Task

This problem solving task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

Type: Problem-Solving Task

## Tutorial

This GeoGebraTube interactive worksheet shows you the step by step method for constructing tangent lines to a circle from a point outside the circle. Use the slider to see each step, and read below the illustration to follow the steps.

Type: Tutorial

## Virtual Manipulative

In this GeoGebraTube interactive worksheet, you can watch the step by step process of circumscribing a circle about a triangle. Using paper and pencil along with this resource will reinforce the concept.

Type: Virtual Manipulative

## Worksheet

This problem solving task shows how to inscribe a circle in a triangle using angle bisectors.

Type: Worksheet

## Parent Resources

## Problem-Solving Tasks

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Type: Problem-Solving Task

This problem solving task challenges students to describe and compare different angles.

Type: Problem-Solving Task

This problem solving task asks students to explain certain characteristics about a triangle.

Type: Problem-Solving Task

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem.

Type: Problem-Solving Task

This problem solving task asks students to place a fire hydrant so that it is equal distance from three given points.

Type: Problem-Solving Task

This problem solving task challenges students to place a warehouse (point) an equal distance from three roads (lines).

Type: Problem-Solving Task

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle.

Type: Problem-Solving Task

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment.

Type: Problem-Solving Task

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Type: Problem-Solving Task

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Type: Problem-Solving Task

This problem solving task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

Type: Problem-Solving Task

## Worksheet

This problem solving task shows how to inscribe a circle in a triangle using angle bisectors.

Type: Worksheet