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CIRCLE&CHEAT&SHEET&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&GEOMETRY&–&MR.&FITTS&& &&&&& Central&Angles: The$measure$of$a$ central$angle$is$equal$ to$the$measure$of$the$ intercepted$arc. Inscribed&Angles: A)$The$measure$of$ an$inscribed$angle$is$ half$the$measure$of$ the$intercepted$arc. $ B)$An$angle$inscribed$ in$a$semicircle $must$be$a$right$angle. $ C)$Inscribed$angles$ that$intercept$the$ same$ arc$are$congruent. $ D)$Inscribed$angles$ that$intercept$ congruent$arcs$are$ congruent. $ E)$Parallel$chords$ intercept$ congruent$arcs.$ $ & Congruent&Chords: A)$Congruent$chords$ intercept congruent$ arcs. $ B)$Congruent$chords$ are$equidistant$ to$the$center$of$the$ circle. Perpendicular& Bisectors&of&Chords: A$perpendicular$ bisector$of$a$ chord$must$go$ through$the$center$ of$the$circle. Tangent&Lines: A)$A$tangent$line$ and$a$radius$are $perpendicular. B)$Tangent$segments$ from$the$same$ external$points$are$ congruent.$ C)$An$angle$formed$by$ a$chord$and$a$$tangent$ line$at$the$point$of$ tangency$is$half$the$ measure$of$the$ intercepted$arc.
CIRCLE&CHEAT&SHEET&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&GEOMETRY&–&MR.&FITTS&& &&&&& Floating&Angles:& A)$The$measure$of$ an$angle$formed$ by$two$lines$that$ intersect$inside$a$ circle$is$the$ average$of$the measure$of$the$ intercepted$arcs. & x = y + z 2 B)$The$ measure$of$an$ angle$formed$ by$two$lines$ that$intersect$ outside$a$ circle$is$half$ the$difference of$the$ intercepted$arcs.$ x = z − y 2
Vocabulary: $ Major$Arc:$$An$arc$measuring$ greater$than$180$degrees & Minor$Arc:$$An$arc$measuring$less$ than$180$degrees$ Central$Angle:$An$angle$formed$by$ two$radii$with$it’s$vertex$at$the$ center$of$the$circle$ Chord:$A$line$segment$whose$ endpoints$both$lie$on$the$circle$ Lengths&of&Segments&of&Chords,& Secants&and&Tangents: $ A)$Chord$Segments: If$two$chords$intersect,$the$product$ of$the$measures$of$the$segments$of$ one$chord$is$equal$to$the$ project$of$the$measures$of$ the$segments$of$the$other. ab = cd B)$Secant$Segments: If$two$secant$segments$are$drawn$to $a$circle$from$an$external$point,$then$ the$product$of$the$lengths$of$one$ secant$segment$and$its$external$ segment$is$equal$to$the$product$of$ the$lengths$of$the$other$secant$ segment$and$its$ external$segment. a ( a + b ) = c ( c + d ) C)$TangentLSecant$Segments If$a$tangent$and$a$secant$are$drawn $to$a$circle$from$an$external$point,$ then$the$square$of$the$length$of$the$ tangent$segment$is$equal$to$the$ product$of$the$length$of$the$secant$ segment$and$its$external$segment. a 2 = b ( b + c ) &
