- is a tangentto the circle
- is a tangentto the circle
- is the centerof the circle
- Prove
Proof.
We will use a similarfigureto the one we usedwe usedto provethe tangentsegmentstheorem(pictured
above).
by congruence.Therefore,.Example 6
Showthat the lineis tangentto the circle
. Find an equationfor the line perpendicularto the tangentline at the pointof tangency. Showthat this line
goesthroughthe centerof the circle.
To checkthat the line is tangentto the circle,substitutethe equationof the line into the equationfor the
circle.