Learning

Lessons

1. Basics
2. Deductive Reasoning

3 - Parallel lines

4 - Congruent Triangles

5 - Quadrilaterals

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.