Geometry-properties 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 =)