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Thread: Circle Geo Help

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    New Member blu boi's Avatar
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    Question Circle Geo Help

    ABCD is a cyclic quadrilateral. The diagonals AC and BD intersect at right angles at X. M is the midpoint of BC, and MX is produced to meet AD at N.

    a)show that BM=MX
    b)show that <MBX = <MXB
    c)Show that MN is perpendicular to AD


    < < <

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    New Member blu boi's Avatar
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    Re: Circle Geo Help

    pls help

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    Re: Circle Geo Help

    a) since <BXC is 90 deg, B, X, C lie on semi-circle, diameter BC, centre M. .: BM = MC = MX, being radii of this semi-circle.

    b) since BM = MX, MBX is an isosceles triangle. So base angles MBX and MXB are equal = @ say.

    c) .: <DAC = <DBC = @

    and < CXM = 90 - < MXB = 90 - @

    But < NXA = < CXM = 90 - @ (vertically opp angles)

    .:, in triangle ANX, < ANX = 180 - < NAX - < NXA = 180 - @ - (90 - @) = 90

    .: MN and AD are perp to each other
    Last edited by Drongoski; 21 Sep 2018 at 9:58 AM.
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