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## Proving Relationships

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**Proving Relationships**October 2007**Homework Quiz**Page 235 5 (c) Page 237 14 (a) Page 295 12 (b) Page 237 15 (a)**A neon sign is to be designed using a team logo. The**diameter of the sign is to be 6.0m. A separate section of neon tubing is to be used for each arc. The designers need to know the length of each tube. They know that the central angle of the logo is 120°, and the two chords are congruent.**Remember the following:**• If two chords are congruent, then the arcs they subtend are also congruent. • If two chords are congruent, then the central angles that they subtend are congruent • If minor arcs are congruent, then the chords formed by joining the endpoints of each arc are congruent**More Properties**• If two parallel lines intersect a circle, then the arcs of the circle between the parallel lines are congruent. c a d b**If an angle is formed by two chords in a circle, then the**measure of the angle is half the sum of the measure of the arc intercepted by the angle and the measure of the arc intercepted by its vertical angle More Properties**Tangent**A line that touches a circle at only one point Secant A line that intersects a circle at two points New terms**If an angle is formed by a tangent to a circle and a chord,**one of whose endpoints is the point of contact (tangency), then the measure of the angle is half the measure of its intercepted arc. New Properties**Sector**The part of the interior of a circle bounced by two radii and an arc between them. Segment The part of the interior of a circle bounded by the circle and a chord. New Terms Minor Arc Major Arc**A cone has a height of 24.0 cm and a radius of 18.0 cm. To**construct the cone, a sector is cut from a circle, then the cut edges are joined. Find the slant height of the cone. (This is the radius of the flattened shape, or sector.) b) Find the circumference of the base of the cone. This is the arc length of the sector. #23 page 239**c) Find the circumference of the flattened circle before the**sector is cut out. Find the ratio of the arc to the total circumference Find the area of the sector**1695.5cm2**0.6πr2 0.6π(30)2