Lessons

1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

Circles (construction)

Objective:

• To be able to construct a tangent to a circle, tangent from a point outside of a circle, circumscribe a circle around a triangle, and inscribe a circle in the triangle.

Lesson 10-5 Circles

Circles can also be constructed. In this lesson you will find out how. Let's begin by forming a tangent to a circle.

 Construct: Tangent to Circle O 1. Draw ray QA 2. Construct the line  |  to  ray OA at A.
 Construct: Tangent from outside point 1. Draw segment OP 2. Find the midpoint M of segment OP by constructing the perpendicular bisector of segment OP. 3. Using M as center and MP as radius, draw a circle that intersects circle O in a point X. 4. Draw ray PX.
 Construct: Circumscribed circle around a triangle 1. Construct the perpendicular bisectors of any two sides of triangle ABC. Label the point of intersection O. 2. Using O as center and OA as radius, draw a circle.
 Construct: Inscribed circle in the triangle. 1. Construct the bisector of angle A and angle B. Label the point of intersection I. 2. Construct a perpendicular from I to segment AB, intersecting segment AB at a point R. 3. Using I as center and IR as radius, draw a circle.

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