2. Properties of radius and chords

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Presentation transcript:

2. Properties of radius and chords Segments in Circles Do Now 3/2: Agenda 1. Do Now 2. Properties of radius and chords 3. Wagon wheel problem 4. Debrief

Find the Rest of the Wagon Wheel

Tangents Draw non-examples of a tangent.

Radii and Chords Draw a diameter Draw a chord perpendicular to the diameter.

Properties of Radii If a radius and a tangent meet at the point of tangency then they form a 90 degree angle. If a radius and a chord meet at 90 degrees, then the radius bisects that chord. **MUST BE IN NOTES!**

Segments in Circles DO NOW 3/3: Agenda 1. Do Now 2. Wagon Wheel Problem 3. Properties of Tangents 4. Check for Understanding/Debrief

Wagon Wheel Problem What is the diameter? 2. If this is a 1:12 scale drawing, what was the size of the actual wheel?

Properties of Tangents Using what we know about properties of radii and tangents, determine the measures of segments QN and MN. If two tangents meet at a common point, the segments (from the point of tangency to that common point) are congruent. **MUST BE IN NOTES!**

Independent Practice / Debrief

Segments in Circles: Chords Do Now 3/4: 1. Do Now/HW Review 2. Derivation of Chords Formula 3. Properties of Chords 4. Geogebra Examples 5. Debrief

HW Review: CYU #2-6

Derivation of Chord Formula Draw two chords MA and TH that intersect at point O. Draw MT and AH. What do we know is true about △MOT and △HOA? Set up a proportion using the sides of the similar triangles. Cross multiply and solve.

Properties of Chords If two chords intersect in a circle, then the product of the two segments of one chord equal the product of the two segments of the other chord. **MUST BE IN NOTES!**

Independent Practice/Debrief

Segments in Circles: Chords (2) Do Now 3/5: Find the length of BC if DE = 32cm, AG=12cm and AF = 9cm. Agenda 1. Do Now 2. Segment Properties Quiz 3. Intersecting Chords in Circles Practice 4. Geogebra Demo/Debrief

Intersecting Chords Practice Use the formula AB * BC = DB * BE where AC and DE are chords that intersect at point B.

Segments in Circles: Secants Do Now 3/6: Find the length of x. Agenda 1. Do Now 2. Geogebra Example/Derive Secant Formula 4. Secant Example and Guided Practice 5. Independent Practice/Debrief

HW Review

Derivation of Secant Formula Draw chord GH and IF. Mark congruent angles. What is true about △GHE and △IFE? Write a proportion using the secants. Cross multiply to solve. **MUST BE IN NOTES!**

Secant Lengths in Circles (Guided Practice)

Independent Practice/Debrief