The measureof an Angleoutsidea circleis
equalto half the differenceof the measures
of the interceptedarcs
The measureof an exterioranglein a trian-
gle equalsthe sum of the measuresof the
remoteinteriorangles
Combiningthe two stepsabovealgebraTherefore, by the AA similaritypostulate.In similartrianglesthe ratiosof correspondingsidesare equal.Example 3
Find the valueof the variable assumingthat it representsthe lengthof a tangentsegment.LessonSummary
In this section,we learnedhow to find the lengthsof differentsegmentsassociatedwith circles:chords,
secants,and tangents.We lookedat casesin whichthe segmentsintersectinsidethe circle,outsidethe
circle,or whereone is tangentto the circle.Thereare differentequationsto find the segmentlengths,relating