Posted by **Kat** on Thursday, March 25, 2010 at 10:56pm.

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.

- Geometry-properties of tangents of a circle -
**Damon**, Friday, March 26, 2010 at 11:01am
<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

- Geometry-properties of tangents of a circle -
**Prarthana**, Sunday, March 28, 2010 at 5:55am
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 =)

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