and are both isoscelesright triangles,therefore and all the
correspondingsidesare proportional:
We can find the lengthof by usingone of the ratiosabove:Cross-multiplyto obtain:Rationalizethe denominators:The lengthof the hypotenuseis +Corollaryto TangentSegmentsTheorem
A line segmentfrom an externalpointto the centerof a circlebisectsthe angleformedby the tangentseg-
mentsstartingat that sameexternalpoint.
Proof.
- Given: