Segment Relationships in Circles | Assignment

University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2022
Views:

92

Pages:

3
Author:

GalacticGuru

Gеошеtгу Segшe11t Relatio11sl1ips i11 Ciгc1es I. Chord- Chord Product Theoreш HYPOTHESIS THEOREM lf t\NO crюrds iпtersect ir1 Н1е iпtNior· of а cir·cle, tr·1eп the proc1uct·s of t.he leщJths of tt1e segtne1·,ts of ti-1e cr,orcls at·e eчual. CONCLUSION АЕ• ЕВ= СЕ• ED Ехашрlе #1: Find tЬе value of х апd tЬе 1e11gth of each choгd. А .Х ·-�- ...,'J..,, . ·"'\i с::; .... ,•' - ('''>tti,,,. ·•····---.,�,.,.••"·• ..... �·-· \ , , : ::: � � А r � f ! \.r . \,, . "··-- � ..( ,,,,...,,.,... '·\,,�'"'' t,.. ) •,!';'"''' . .,, ' . .. \. .,,q .� ·"' ·•,., '°' 'i i"'iii . , , ./ Ехашр1е #2: The агt departmeii 1s c�ntracted to co11struct а woodeп 1110011 for а play. One of the aiiists creates а sketch of wЬat it пeeds to look like Ьу drю:vi11g а chord апd its perpe11dicular Ьisectoг. Fiпd the diameter of the cjrcle used to draw the outer edge of the 1110011. / j-q 8 iп. / �--q ! - 1 х ..- \ oL в II. Secant - Secant P1�oduct Theorem А secant segment is а segmeпt of а secant with at least опе eпdpoiпt on tЬе circle. An ехtегпаl secant segшent is а secaпt segmeпt that lies i11 the exterior of the circ]e with one endpoi11t 011 the circle. f 1V.Л1 , 1(1\,,1) ап cl ]Л1 аге secaпt segп1eпts оУ 0(). J\fJ\1[ а11с1 ]Л-1 аге ехtегпаl secaпt seg111e11ts. РЛ1J \ THEOREM lf tvvo secaпts intersect iп the exterioг of а ci гсlе, tl1en tl1e product of Н1е leпgtl1s of опе se-caпt se-g111eг1t апс1 its exterпal segгnent eqLшls Н1е prodL;ct of tl'1e leпgtl,s of t�1e otl1er secaпt se�Jmeпt апс! its ехtегпаl sе9п1епt. (v\/1-юle • OLJtsic!e = 'Nrюle • outside) HVPOTHESIS CONCLlJSION Secaпts А{ апсi СЁ iпte-rsect at Е. Exa111ple #3: Fi11d the value of х апd the leпgth of еасЬ secant segmeпt. G А tangent segment is а segmeпt of а tangent with one e11dpoi11t 011 the circle. АВ and А С aie taпgent segmeпts. Secant-Tat1ge1·1t Product тt,eoren-r HYPOTHESIS --· ------------+-----------....... --,CONCLUSION THEOREM lf а secant апd а t.anger,t ir1tersect in the exterior of а с i r с I е tr, е п t h е р r о d LJ ct о f ·tJ1e lengtr1s of tr,e secant seg гпеnt. апd its exteгnal segrnent ec1uals the length of tf-')e tan�Jer,t segtr1ent sqLJared. (1,,�Jhole • outsicJe = ta пgent 2 ) I Ехашрlе #4: Find tЬе value of х. L к -· 1./ х' -· \. (,·.·� АС• ВС = DC 2 Secant АС апd tangent DC inteгsect a·t С