# Tangent to a Circle From a Point

##### This Tangent to a Circle From a Point activity & project also includes:

Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using information about both to describe a situation. A great quickie problem to help remind learners that just because a property looks evident doesn't mean it can just be stated without proof.

CCSS: Designed

##### Instructional Ideas

• Use before and after teaching construction techniques as a motivator or reward
• Use as a refresher problem on circle or tangent properties as part of a larger review
##### Classroom Considerations

• Student task is not separated from teacher notes and solution key
##### Pros

• Elegant solution pulls from both triangle and circle properties to reach conclusions
• Good example of using mathematical rigor to defend and prove something that seems evident from a diagram
##### Cons

• Though introduced as a construction problem, no actual construction is performed—just using definitions to describe what is shown in a diagram
• The circles are named C and D, but only diagrammed by the centers O and M, making them hard to follow through the explanations