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Tangent,Secant, Chords

Chords,Secants

Circumference

Area of Circles

Circles: Diameter

Surface Area of a Sphere

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Lesson 1: Circles, Tangent, Secants, and Chords

 

Lengths of the tangents explained

Rules for two tangents drawn to a circle

Finding the perimeter of a triangle using tangents of a circle

Formula for chords explained

Application problem using the formula for chords

Formula for secants ( The product of the lengths of the secant segment and its external segment is equal to the product of the lengths of the second secant segment and its external segment

Formula for secants explained

Application problem using one secant and one tangent

Example problem using a circle, tangent, and a secant

 

 

Lesson 2: Circles, Chords and Secant Segments

Sample problem- solving for a chord in a circle

Problem using a radius, and the rules for secant in order to find the length of a tangent.

Problem involving connecting secant segments

Sample problem with secants and the interior and exterior secant

Problem involving secant segments

Problem involving the outside secant segment and the whole secant segment. This problem involves solving a quadratic equation

Sample problem involving a secant and a tangent

 

 

Lesson 3: Finding the circumference of a circle and arc Length

Formula for circumference of a circle explained

Definition of circumference

Formula for circumference involving radius explained

Sample problem-find the circumference of a circle

Arc length formula explained

Sample problem-finding the arc length of a circle

Sample problem-finding the arc length of a circle when given the diameter and the central angle

Sample problem-find the radius of a circle given the arc length

Answer to sample problem

 

 

Lesson 4: Finding the area of a circle and the sector area

Definition of a sector

Formula for area of a circle

Sample problem- finding the area of a circle when given the radius

Sample problem - finding the area of a circle when given the diameter

Formula for area of a sector explained

Sample problem - find the area of a sector

Sample problem - find the area of a sector

Sample problem- find the area of a circle given the sector area

Sample problem - find the radius of a circle given a central angle and the sector area

 

 

Lesson 5: Finding the circumference, diameter, and radius of a circle

Word problem in which you find the diameter of a circle using the arc length. This problem is solved by setting up a proportion of the arc length over circumference equaling the measure of the angle over 360 in order to find the circumference. You then use the circumference to find your diameter.

Word problem in which you find the circumference of a circle using the radius.

This problem uses the circumference formula in order to find the circumference of the circle using the radius.

The last word problem involves a clock and how many degrees the clock travels in a certain amount of time. The solution involves finding how many degrees the hand of the clock travels per minute.

Each word problem is solved and step by step directions are given for each solution.

 

 

Lesson 6: Finding the surface area and the volume of a sphere

Definition of a sphere

An example of the definition of a sphere

Radius of a sphere explained.

The great circle explained with an illustration

Definition of hemisphere and a brief explanation of hemisphere

Formula for surface area of a sphere

Formula for volume of a sphere

Sample problem with step by step instruction over how to find the surface area of a sphere.

Example problem with step by step instructions for finding the volume of a sphere.

 

 

 

 



Check the Table of Contents for a list of all of the topics covered

High School Geometry Circles:Area,Circumference,Diameter

Here is a quick list of topics covered in this circle unit. Circles, tangent, secants, chords and secant segments, finding the circumference of a circle and arc length, finding the area of a circle, and the sector area, finding the surface area and the volume of a sphere, and finding the circumference, diameter, and radius of a circle.