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