Segments in Circles: Secants and Tangents DO NOW: 3/9 Find the measure of x. Segments in Circles: Secants and Tangents Agenda 1. Do Now 2. Geogebra Investigation 3. Tangent Segment Derivation 4. Independent Practice/Debrief

GeoGebra Investigation Complete Part 1 and 2 We will use the chart below to record class measures and come up with equations (questions #3 and 4) Complete Part 3 independently, and compare to answer questions #3 and 4 AE CE BE DE

Guided Practice

Independent Practice

Segments in Circles: Practice Do Now 3/10: Find the measure of x. Agenda 1. Do Now 2. Segments in Circles Equations 3. Segment in Circles Carousel 4. Exit Ticket

Segments in Circles Equations Chord Lengths - (chord segment 1)x(chord segment 1) = (chord segment 2)x(chord segment 2) Secant Lengths - (whole secant 1)x(external secant 1) = (whole secant 2)x(external secant 2) Tangent/Secant Lengths - (whole secant 1)x(external secant 1) = (tangent)x(tangent)

Segments in Circles Carousel 1. Label each diagram with points and additional information (segment additon, etc.) 2. Write appropriate equation based on types of segments in circles. 3. Solve equation and check answer.

Exit Ticket

Secant Segments in Circles: Special Case Do Now 3/11: Find the measure of x. Agenda 1. Do Now 2. Secant Segments with Quadratics 3. Solving Quadratics by Factoring 4. Independent Practice/Debrief

Secants: Quadratic Cases When the external secant segment is unknown (a variable) it is likely that we will end up with an equation in the form of a quadratic. (a)x2 + (b)x + (c) = 0 One way to solve these equations is by factoring.

Steps to Factoring Simple* Quadratics Put into standard (a)x2 + (b)x + (c) = 0 form. Identify factors of the (c) term. Look for factors that also combine to equal the b term. Set up two sets of parentheses ( ) ( ) and put the factor of your (a) term in the front of each. Put the two factors from step 3 in the end of each parentheses. How to determine signs: If (c) is positive, the signs in both parentheses are the same; match them with the sign of (b) If (c) is negative, the signs in both parentheses are different; match the sign of the bigger factor with the sign of (b)

Guided Practice with Factoring

Independent Practice/Debrief Well that was a fun trip down Algebra Memory Lane! …Now back to Geometry and Circles. How does this apply to the problem we saw earlier?

2. Quiz: Segments in Circles Do Now 3/12: Find the measure of x. Agenda 1. Do Now 2. Quiz: Segments in Circles 3. Embedded Assessment 4. Debrief

Happy (Day Before) Pi Day! 3/14/15 @ 9:26:53 Do Now 3/13: 𝜋≈ Agenda Embedded Assessment Questions (#1) Calculate Circumference/Diameter of Pi Find Area/Eat circular foods Pi paper chain

Embedded Assessment The circular track is tangent to each side of Quad ABCD A and all of the angles in Quad ABCD are right angles. W, X, Y, and Z are the points of tangency. Find each of the following. m 𝑍𝑊 m 𝑊𝑋𝑍

Derivation of Pi ITEM CIRCUMFERENCE (C) DIAMETER (d) RATIO (C/d)