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Classzone.com has been retired and is no longer accessible. Because of the age of this application, the programs supported by this platform are not able to benefit from the technological improvements in accessibility, security, and HMTL5 (non-Flash) that we have incorporated into our newer programs and platforms in recent years.Learn more about HMHs newest classroom solutions.If you want to retrieve your user data from the platform that is no longer accessible, please contact <EMAIL> or <PHONE> and let us know that youre contacting us about user data extraction from Classzone.com.Please note, user data extraction does not include program content. This page: Top Applet Practice (tan and sec) 2 Secants 2 Secants Practice Formula: If a secant and a tangent of a circle are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment. Use the theorem for the intersection of a tangent and a secant of a circle to solve the problems below. In this diagram, the red line is a tangent, how long is it? $ red x^2 = (7 + blue 5) cdot blue 5 red x^2 = ( 12 ) cdot blue 5 red x^2 = 60 red x = sqrt60 $ $ red x^2 = (9+ blue 7) cdot blue 7 red x^2 = (16) cdot blue 7 red x^2 = 112 red x = sqrt 112 $ This page: Top Applet Practice (tan and sec) 2 Secants 2 Secants Practice Formula: If two secant segments are drawn from a point outisde a circle, the product of the lengths (C + D) of one secant segment and its exteranal segment (D) equals the product of the lengths (A + B) of the other secant segment and its external segment (B). Use the theorem above to determine A if $$ B = 4, C = 8, D = 5 $$ . $ (A + blue 4) cdot blue 4 = (8 + blue 5) cdot blue 5 (A + blue 4) cdot blue 4 = (14 ) cdot blue 5 (A + blue 4) cdot blue 4 = 65 frac 1 4 cdot (A + blue 4) cdot blue 4 =frac 1 4 cdot 65 frac 1 cancel 4 cdot (A + blue 4) cdot blue cancel 4 = 16.25 A + blue 4 - 4 = 16.25 - 4 A = 12.25 $ Use the theorem above to determine A if $$ B = 8, C = 16, D = 10 $$. $ (A + blue 8) cdot blue 8 = (16 + blue 10) cdot blue 10 (A + blue 8) cdot blue 8 = (26) cdot blue 10 (A + blue 8) cdot blue 8 = 260 frac1 8 cdot (A + blue 8) cdot blue 8 = frac1 8 cdot 260 (A + blue 8) = 32.5 A = 32.5 - 8 A = 24.5 $ The two secants in the picture below are not drawn to scale. If $$ KO = 16$$, $$ KJ = 4 $$, and $$ LO = 32$$ , what is $$LM$$ ? The first challenge here is for you to recognize that the side lengths we are given are not the ones that we can use for the formula!!. Please see the diagram below, which labels the measurements that we are given.: What we need to know is the length of $$overline JO$$ and $$ MO$$ ! So, the first thing we must do is is figure out the portion of the secants that are outside the circle. $ color#666600 JO = 16 - 4 = 12 textNow, apply formula : KO cdot JO = LO cdot MO 16 cdot 12 = 32 cdot MO 192 = 32 cdot MO frac 19232 = frac3232 cdot MO 6 = MO textNow, question asks for LM LM = LO-MO LM = 32 - 6 = boxed 26 $ Related Pages: If youre seeing this message, it means were having trouble loading external resources on our website. If youre behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. © 2022 Kuta Software. All rights reserved. See a bug? Let us know! Here you can also share your thoughts and ideas about updates to LiveJournal Your request has been filed. You can track the progress of your request at: If you have any other questions or comments, you can add them to that request at any time. Send another report Close feedback form Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. There are over 85 topics in all, from multi-step equations to constructions. Suitable for any class with geometry content. Designed for all levels of learners, from remedial to advanced. Adding and subtracting square roots Line segments and their measures Segment Addition Postulate Angles and their measures Geometric diagrams and notation Parallel lines and transversals Points of the coordinate plane Graphing linear equations Proving triangles congruent Isosceles and equilateral triangles Triangle Inequality Theorem Inequalities in one triangle Area of triangles and quadrilaterals Proportional parts in triangles and parallel lines Multi-step Pythagorean Theorem problems Multi-step special right triangle problems Multi-step trig. problems Rhombuses and kites with right triangles Solid figures: identifying, volume, and area Naming arcs and central angles Measures of arcs and central angles Arc length and sector area Secant and tangent angles Using equations of circles Writing equations of circles Translations, rotations, and reflections Sample spaces and the Fundamental Counting Principle Probability of independent and dependent events, word problems Probability of independent and dependent events Probability of mutually exclusive events, word problems Probability of mutually exclusive events Permutations vs combinations Probability with permutations and combinations

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