8.2: Properties of a Chord Circle Geometry. What is a chord?  a chord is line segment joining two endpoints that lie on a circle.

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Presentation transcript:

8.2: Properties of a Chord Circle 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

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….  /chordBisector.htm /chordBisector.htm  le/chord-perpendicular-bisector.html le/chord-perpendicular-bisector.html

Let’s get crazy… b Find b.

Let’s get crazy… b Step 1: What do we need to find? We need a radius to complete this big triangle. Find b.

Let’s get crazy… b Find b. How do we find a radius? We can draw multiple radii (radiuses).

Let’s get crazy… b Find b. How do we find a radius? Now what do we have and what will we do?

Let’s get crazy… b 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 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 Find b. !!!Pythagorean Theorem!!! a 2 +b 2 =c 2 so =169 so b is

Assignment Time  Pg , 4, 5, 6, 7, 10, 11, 18, 19(Draw it out!)