1. Sec 4.4 – Circles & Volume Circle Segments Name:
Intersecting Chords
Considertheintersectingchords and thatintersectatpointB.
Drawanauxiliarysegment and tocreatetriangles∆DBEand∆FBC.Weknowthat∡ ≅ ∡ becausetheyarebothinscribedanglesthatinterceptthesamearc .Similarly,weknow∡ ≅ ∡ .Then,byAAweknow
∆ ~∆
Usingproportionsofsimilartriangles:
Wecancross‐multiplytogiveusthefollowingstatement:
∙ ∙
“Iftwochordsintersectthentheproductofthemeasuresofthetwosubdividedpartsofonechordareequaltotheproductofthepartsoftheotherchord.”
Findthemostappropriatevaluefor‘x’ineachofthediagramsbelow.
1. 2.
3. 4.
x = x =
M.Winking Unit4‐4page99
x = x =
Part1 Part2 Part1 Part2
Findthemostappropriatevaluefor‘x’ineachofthediagramsbelow
5. 6.
Segments of Secants
Considertheintersectingsegmentsofsecants and
thatintersectatpointC.
Drawanauxiliarysegment and tocreatetriangles∆ADCand∆EBC.Weknowthat∡ ≅ ∡ becausetheyarebothinscribedanglesthatinterceptthesamearc .Reflexively,wealsoknow∡ ≅ ∡ .Then,byAAweknow
∆ ~∆
Usingproportionsofsimilartriangles:
Wecancross‐multiplytogiveusthefollowingstatement: ∙ ∙
“If2secantsintersectthesamecircleontheexteriorofthecirclethentheproductofthe‘whole’and
the‘external’segmentmeasuresisequaltothesameproductoftheothersecant’sportions.
Findthemostappropriatevaluefor‘x’ineachofthediagramsbelow.
7. 8.
x = x =
Whole External Whole External
x = x =
M.Winking Unit4‐4page100
Findthemostappropriatevaluefor‘x’ineachofthediagramsbelow.
9. 10.
11. 12.
Segments of Secants and Tangents
Considertheintersectingsegmentofasecant andsegmentofatangent that
intersectatpointA.
Drawanauxiliarysegment and tocreatetriangles∆ADCand∆ABD.Weknowthat∡ ≅ ∡ becausetheyarebothhaveameasureofhalfoftheinterceptedarc .Reflexively,wealsoknow∡ ≅ ∡ .Then,byAAweknow
∆ ~∆
Usingproportionsofsimilartriangles:
Wecancross‐multiplytogiveusthefollowingstatement: ∙ ∙
x = x =
x = x =
Tangent Whole External Tangent
M.Winking Unit4‐4page101
Findthemostappropriatevaluefor‘x’ineachofthediagramsbelow.
13. 14.
Findthemostappropriatevaluefor‘x’ineachofthediagramsbelow.
13. 14.
x = x =
∙ ∙
Whole External Whole External Part1 Part2 Part1 Part2
∙ ∙ ∙
Whole External Tangent 2
x = x =
M.Winking Unit4‐4page102