Geometryproperties of tangents of a circle
posted by Kat on .
Circle L has segment LJ and segment LK as radii. Those 2 segments are perpendicular. Segment KM and segment JM are tangent to circle L. Is triangle JLM congruent to triangle KLM? Please explain.

<KLJ is right given
<LKM = <LJM is right (tangent to circle perpendicular to radius)
MJ  KL and KM  LJ congruent interior and exterior angles (all right angles)
the remaining angle in the square is right and all sides are equal .
therefore LM is diagonal of square
diagonal cuts  lines so opp interior angles JML=KLM =JLM=KML
angles the same and hypotenuse the same and radii the same, side angle side 
TriangleJLM, Triangle KLM
JM=KM as Length of tangents to a circle from external point is equal
Also LJ=LK as they are radii of circle
LM is common side!
Hence by SSS congruency principle the 2 triangles are congruent =)