Victory for the ACT Exam 16e TG Sample

U NIT 4 | G EOMETRY • 515

STUDENT TEXT, pp. 187–188 17. The �igure below shows two pulleys cpounl lneeycstaerdeb8y fae ebteal tp. aI fr tt haen dc etnhtee pr su ol lfe yt hs e eleancghthh,aivnefaeerta,doifutshoef b1eflot?ot , what is the

EXPLANATIONS

17. (D) Mathematics/Geometry/Properties of Tangent Lines and Circles CC: HSG-MG.A.1 CCRS: EXP.G.5 Difficulty Level = 4; Teaching Time = 5–8 minutes; Purpose = Example At o l ei ni tehde rr aowf nt hfer opmo i nt ht se ocfe tnatne gr eonf ceyi twh ei lrl p u l l e y ct wr eoa tset raa i9g0h°t as ne cg tl ei o. nTsh ou fs ,8t hf eee bt ee lat ccho, npsl ui sst st wo fo semicircles of radius 1 foot: length belt = Properties of Tangent Lines and Triangles/30° − 60° − 90° Triangles and Properties of Triangles CC: HSG-SRT.C.6 CCRS: ADV.G.3 Difficulty Level = 4; Teaching Time = 5–8 minutes; Purpose = Walkthrough Dt r ri aanwg lae raat dt hi ue spioni nt et rosfetcatni ng eg ntchye t soi dt hee ocfi rtchl ee: (2)(8) 2 (2 ) 16 2 (1) 16 2 r . r r r 2 1 ` j 18. (J) Mathematics/Geometry/ To nhee sr iedseu lot f i lsean g3t0h° -16. 0T°h- 9e 0s°i dt er i oa np gploeswi t ei t ht h e 60° angle has a length of 3 0 . Therefore, tehqeuilleantgetrhalotfritahnegsliedies of the circumscribed 2 3 , and the perimeter is 3 2 3 6 3 = ^ h . As tlrt ae trengayt i cvaenl y b, teh ae p“pe ll ii emdi nh ae tree- awni dt h- ggureesast ” spur oc cvei ds se.dBians tehdeodnr at hwei ni ngf, oi tr mi s aotbi ovni o u s t h a t ot rni aen- hgal el f ios fgorne ae tseirdtehoafnt thheeerqaudiilua st eorfa tl h e it nr isacnr gi bl ee dmcui sr ct lbe e. Sgor,etahtee rp tehr ai mn e6t e( trhor fe teh e sgirdeeast ,eer atchha no ft ww ihciec ht hhearsaad il ue ns gotfht ht heacti ri sc l e ) . Tfohre(rJe)fcoarne, baell eolfimthienaatnesdw. er choices except

A. 4 0 r B. 8 0 r C. 8 0 + r D. 16 2 + r

18. In the �igure below, a circle is inscribed itnh ea nc i recqlue i il sa t1e, rwa lhtar ti ai ns gt hl ee. Ipf etrhi emreatde iruosf ot fh e triangle? F. 3 0 G. 2 3 H. 3 3 0 J. 6 3