Loudoun County Public Schools



SOL G.11The student will use angles, arcs, chords, tangents, and secants to a) investigate, verify, and apply properties of circles; b) solve real-world problems involving properties of circles; and c) find arc lengths and areas of sectors in circles.? Find lengths, angle measures, and arc measures associated with– two intersecting chords;– two intersecting secants;– an intersecting secant and tangent;– two intersecting tangents; and– central and inscribed angles.? Calculate the area of a sector and the length of an arc of a circle, using proportions.? Solve real-world problems associated with circles, using properties of angles, lines, and arcs.? Verify properties of circles, using deductive reasoning, algebraic, and coordinate methods.WHAT I NEED TO KNOW:FORMULAS (AREA AND CIRCUMFERENCE ON FORMULA SHEET)AREA OF SECTORLENGTH OF AN ARC1143007112000Part of areamo of arc ? πr2 360o1600207112000Part of circumferencemo of arc ? 2πr 360oLENGTHSINTERSECTING INSIDE OF CIRCLEINTERSECTING OUTSIDE OF CIRCLE013589000101727013589000PP = PPab = cd1156335215900086233017589500OW = OWaa = b(b+c)a(a+b)=c(c+d)coneheadAC = ABANGLE MEASURESINSIDE8001019113500OUTSIDECENTRALON33147019050027432062865004686306286500Angle = arc + arc 2Angle = arc – arc 2Angle = arcAngle = arc 2CONGRUENT CHORDSANGLE BETWEEN TANGENT AND RADIUSIf chords are congruent, then the intercepted arcs are congruent.The angle between the tangent and the radius is 90oG.11 PROBLEMS:-1143001384300033147004826000320040019304000398145019939000377190085090-3429008509001092200020574001333500034290043180004229100190520.3 sq. ft.20.3 sq. ft.2743200260353434-3429001885955143500984250011430098425005029200153035002743200-3175-22860011112500297180011112500-342900-3175-228600952500377190014795518 cm18 cm ................
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