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Math Help - Circle Theorum

  1. #1
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    Circle Theorum

    Angle B = 32

    find Angle MOC

    but how do i find MOC and what is the rule?

    ----

    Please note: O IS the centre of the circle
    ---
    tri-2.jpg picture by jsmith613 - Photobucket
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  2. #2
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    Quote Originally Posted by jsmith613 View Post
    Angle B = 32
    \color{red} Is\ it\ 32^o\ or \ 37^o\ ?

    find Angle MOC

    but how do i find MOC and what is the rule?

    ----

    Please note: O IS the centre of the circle
    ---
    tri-2.jpg picture by jsmith613 - Photobucket
    AB is a diameter, therefore angle BCA=90 degrees.
    Therefore angle CAO is 90-37=53 degrees.
    Triangle AOC is isosceles as two sides are radius length.
    Therefore angle CAO=angle OCA.
    Also side AC is perpendicular to side OM.

    Angle CBA=37 degrees, so angle MAO is 90-37=53 degrees.
    Therefore angle MCO=53 degrees, angle MOC=37 degrees.

    Or angle BCA is 90 degrees.
    Angle OMA is 90 degrees, therefore line OM is parallel to side BC.
    Hence angle OMA=angle BAC.
    Triangle OCA is isosceles and is split into 2 identical right angled triangles.
    Therefore angle MOA=angle MOC.
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