8.2: Properties of a ChordCircle Geometry

What is a chord?

a chord is line segment joining two endpoints that lie on a circle.

What is a chord?

A circle can have many chords but there is one special chord left to mention

What is a chord?

It turns out that a diameter of a circle is the longest chord of this circle since it passes through the center. A diameter satisfies the definition of a chord, however, a chord is not necessarily a diameter.

Therefore, every diameter is a chord, but not every chord is a diameter.

Working with Chords, Radii and Diameters

http://www.mathgoodies.com/lessons/vol2/geometry.html

Chord Property #1, #2 and #3

A perpendicular line from the centre of a chord to the centre of a circle:

#1: Makes a 90° angle with the chord

#2: Creates two equal line segments RS and QR

#3: Must pass through the centre of the circle O

Chord Property #1, #2 and #3

Let’s play with this….

http://staff.argyll.epsb.ca/jreed/math20p/circles/chordBisector.htm

http://www.mathwarehouse.com/geometry/circle/chord-perpendicular-bisector.html

Let’s get crazy…

b

3 8

12

Find b.

Let’s get crazy…

b

3 8

12

Step 1: What do we need to find?

We need a radius to complete this big triangle.

Find b.

Let’s get crazy…

b

3 8

12

Find b.

How do we find a radius?

We can draw multiple radii (radiuses).

Let’s get crazy…

b

3 8

12

Find b.

How do we find a radius?

Now what do we have and what will we do?

Let’s get crazy…

b

3 8

12

Find b.

How do we find a radius?

We create this triangle but how do we get the missing side?

Let’s get crazy…

b

3 8

12

Find b.

How do we find a radius?

We create this triangle but how do we get the missing side?

4

Let’s get crazy…

b

34

12

Find b.

!!!Pythagorean Theorem!!!

a2+b2=c2 so 52+122=169 so b is 13.

5

513

Assignment Time

Pg. 397-340

3, 4, 5, 6, 7, 10, 11, 18, 19(Draw it out!)