Ex 4: In each diagram, is a radius of circle R. Is tangent to circle R? a.) TR = 26 b.) UT = 8 Ex 5: In the diagram, B is a point of tangency. Find the radius r of circle C. Theorem 10.2: Tangent segments from a common external point are____________________ Ex 6: is tangent to circle C at R and is tangent to circle C at S. Find the of x Ex 7: is tangent to circle C at S and is tangent to circle C at T. Find the value of x. Ex 8: You are standing 36 feet from a circular swimming pool. The distance from you to a of tangency on the pool is 48 feet as shown. What is the radius of the swimming pool? Ex 9: Consider a circle with radius 2. Two are drawn at right angles to each other. A tangent is drawn at each of the points where the radii intersect the circle. How far from the center of the circle do the tangent lines intersect? Express answer as a simplifies radical. Name _____________________________________________________________________ Hour _________ Honors Geometry Lesson 10-2: Find Arc Measures Learning Target: By the end of today’s lesson we will be able to successfully use angle measures to find arc measures. Vocabulary Definitions Illustrations Central angle A central angle of a circle is an angle whose vertex is the ______________ of the circle. Minor arc Part of a circle measuring less than __________. Major arc Part of a circle measuring between ______ and______.
Ex 7: In the diagram below, and are two parallel chords of O. If AB = 6, CD =12 and the distance between these chords is 3, what is the exact value of the radius of O? Name _____________________________________________________________________ Hour _________ Honors Geometry Lesson 10-4: Use Inscribed Angles and Polygons Learning Target: By the end of today’s lesson we will be able to successfully use inscribed angles of circles. Vocabulary Definition Illustrations Inscribed angle An inscribed angle is an angle whose ____________ is on a circle and whose sides contain ________ of the circle. Intercepted arc The arc that lies in the interior of an _______________ angle and has _______________ on the angle is called the intercepted arc of the angle. Inscribed polygon A polygon is an inscribed polygon if all of its ______________ lie on a circle. Circumscribed circle A circumscribed circle is a circle that contains the vertices of an ______________ polygon. Theorem 10.7: Measure of an Inscribed Angle Theorem The measure of an inscribed angle is one half the measure of its_____________________ _______. mADB = ½ • ___________ Ex 1: Find the indicated measure in P. a.) mS b.) measure of arc RQ. Ex 2: Find the indicated measure. a.) b.) c.) x
External segment An external segment is the part of a secant segment that is __________________ the circle. Theorem 10.14: Segments of Chords Theorem If two chords intersect in the ________________ of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. EA • ________ = EC • ________ OR…… _____ • _____ = _____• _____ Ex 1: Find x, ML and JK. Theorem 10.15: Segments of Secants Theorem If two secant segments share the same endpoint _______________ a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. (Whole secant segment • outside segment) = (Whole secant segment • outside segment) EA • ____ = EC • ____ Ex 2: Find the value of x and RT. Ex 3: Find EB and ED Theorem 10.16: Segments of Secants and Tangents Theorem: If a secant segment and a tangent segment share an ____________ ____________a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. (Tangent segment) 2 = (Whole secant segment • outside segment)
1) Write the expression as a square of a binomial. a) x2 + 14x + 49 b) x2 + 18x + 81 2) Find the value of c that makes the expression a perfect square trinomial. Write the expression as a square of a binomial. a) x2 - 10x + c b) x2 + 22x + c c) x2 - 12x + c 3) Find the equation, center, and radius of each circle in standard form. a) x2 + y2 + 2x – 35 = 0 b) x2 + y2 – 8x – 4y + 18 = 0 c) x2 + y2 – 4x + 12y – 7 = 0 d) x2 + y2 – 2x + 6y + 3= 0 Extra stuff found LESSON 10.4 Real-Life Application: When Will I Ever Use This? For use with pages 671–679 Satellite Television Satellite television companies use stationary satellites to transmit programming to their customers. They need the stable coverage to ensure customer satisfaction. The companies must maximize the area covered by each satellite in their network. They want to launch as few satellites as possible to completely cover an area. To do this, they must find out how much of Earth is covered by one satellite. In Exercises 1–6, use the following information. The satellite at points is A a stationary satellite in the network of a satellite television company. It is hovering 400 miles above Earth. The radius of Earth is approximately 4000 miles. Name the central angle that intercepts the arc covered by the satellite. What is the length of ?