Geometry-properties of tangents of a circle

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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 -

    <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 -

    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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