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Math Help - Circle Geometry Solutions Weird

  1. #1
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    Exclamation Circle Geometry Solutions Weird

    In the diagram shown, O and P are centres, LMN is a common tangent and MT a common chord.

    i) Prove that OLMT and PNMT are cyclic quadrilaterals.

    ii) Prove that triangle LMT is similar to triangle TNP.

    For ii), the solution gave:

    In triangles LTM and TNP,
    Angle LMT = Angle TPN (exterior angle of cyclic quad. equal to interior remote angle)
    PT = PN (equal radii)
    LM = MT (tangents from external point equal)
    Therefore, triangle LMT is similar to triangle TNP (corresponding sides about equal angles)

    Could someone explain me how PT = PN and LM = MT works to prove the triangles are similar?

    Thanx a lot!
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  2. #2
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by xwrathbringerx View Post

    Could someone explain me how PT = PN and LM = MT works to prove the triangles are similar?

    Thanx a lot!
    Because \frac{PT}{LM}=\frac{PN}{MT}
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