1. Spi.4.2 Define, identify, describe, and/or model plane figures using appropriate mathematical symbols (including collinear and non-collinear points, lines, segments, rays, angles, triangles, quadrilaterals, and other polygons). Check.4.40 Find angle measures, intercepted arc measures, and segment lengths formed by radii, chords, secants, and tangents intersecting inside and outside circles. CLE 3108.4.9 Develop the role of circles in geometry, including angle measurement, properties as a geometric figure, and aspects relating to the coordinate plane. Spi.4.13 Identify, analyze and/or use basic properties and theorems of circles to solve problems (including those relating right triangles and circles). 10.7 Special Segments in a Circle

2. If two chords intersect in a circle, then the products of the measure of the segments of the chords are equal. AE * EC = BE * ED A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty. Winston Churchill Objective: Find measure of segments that intersect inside and outside of a circle If two secants are drawn to a circle from an exterior point, then the product of the measures of the exterior segment and a secant segments is equal to the product of the other exterior segment and secant segment. AB * AC = AE * AD If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment WX * WX = WZ * WY

3. 10.7 Special Segments in a Circle If two chords intersect in a circle, then the products of the measure of the segments of the chords are equal. AE * EC = BE * ED A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty. Winston Churchill Objective: Find measure of segments that intersect inside and outside of a circle Vertical Angles Two inscribed angles intercepting the same arc Angle- Angle Similarity

4. Intersection of two chords Find X AE*EB=CE*ED X*6 = 3* 4 = 12 X = 2 Find X X*8 = 12* 9 = 108 X = 13.5

5. 24*24 = 12*x 48 = x Diameter = 12 + 48 = 60 Radius = 30 12 48 x

6. 10.7 Special Segments in a Circle A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty. Winston Churchill Objective: Find measure of segments that intersect inside and outside of a circle If two secants are drawn to a circle from an exterior point, then the product of the measures of the exterior segment and a secant segments is equal to the product of the other exterior segment and secant segment. AB * AC = AE * AD Share Angle A Two inscribed angles intercepting the same arc (C, D) Angle- Angle Similarity

7. Intersection of 2 secants Find RS if PQ =12, QR = 2, and TS = 3. Let RS = x 2*(12+2) = x*(x+3) 28 = x 2 + 3x 0 = x 2 + 3x – 28 (x + 7)(x – 4) x=-7, x=4 disregard the negative answer

8. Intersection of 2 secants 10*(10+24) =8*(8+x) 340 = 8x +64 276 = 8x 34.5 = x

9. 10.7 Special Segments in a Circle A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty. Winston Churchill Objective: Find measure of segments that intersect inside and outside of a circle If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment WX * WX = WZ * WY m  XYZ = ½ mXZ m  WXZ = ½ mXZ m  WXZ = m  XYZ AA Similarity

10. Secant and a Tangent Find X, assume segments that appear to be tangent are. 4 2 = x(x +x+2)= x(2x + 2) 16 = 2x 2 + 2x 0 = 2x 2 + 2x – 16 0= x 2 + x – 8

11. Special Segments in a Circle Practice Assignment Page 740 6 – 22 even*, Honors Page 740 10 – 26 even* If two chords intersect in a circle, then the products of the measure of the segments of the chords are equal. AE * EC = BE * ED If two secants are drawn to a circle from an exterior point, then the product of the measures of the exterior segment and a secant segments is equal to the product of the other exterior segment and secant segment. AB * AC = AE * AD Outside*total = outside*total If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment WX * WX = WZ * WY Outside*outside = outside*total