This has a doubleroot at =. This meansthat the line intersectsthe circleat only one point.A perpendicularline to the tangentline wouldhavea slopethat is the negativereciprocalof the tangentline or =.
The equationof the line can be written: = +.We find the valueof by pluggingin the tangencypoint:The equationis and we knowthat it passesthroughthe originsincethe -interceptis zero.This meansthat the radiusof the circleis perpendicularto the tangentto the circle.LessonSummary
In this sectionwe learnedabouttangentsand their relationshipto the circle.We foundthat a tangentline
touchesthe circleat one point,whichis the endpointof a radiusof the circle.The radiusand tangentline
are perpendicularto eachother. We foundout that if two segmentsare tangentto a circle,and sharea
commonendpointoutsidethe circle;the segmentsare congruent.
LessonExercises
- Determinewhethereachsegmentis tangentto the givencircle:
a.b.