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Math Help - Help with a geometry question

  1. #1
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    Help with a geometry question

    I was wondering if anyone could

    1)Check my interpretation/drawing of the question

    2)Help me solve it

    Here is the question:
    A circle with centre P circumscribes triangle ABC (ie: touches each vertex). In the triangle: Angle A=75o and Angle B=60o. Construct tangents at points A and B, and extend them to intersect at D-outside the circle.

    Show that ABD is an isosceles triangle with a right angle at D.

    (Hint: you may need to construct some extra lines within triangle ABC)

    Here is what I believe is described in the first paragraph:
    IMG_0007.jpg picture by alexandersaver - Photobucket

    Could anyone help me solve this( as well as where I would put the xtra lines)

    Thanks
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  2. #2
    MHF Contributor red_dog's Avatar
    Joined
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    Medgidia, Romania
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    You don't have to construct extra lines.

    m(\widehat{DAB})=\frac{m(arcAB)}{2}=m(\widehat{C})  =45^{\circ}

    m(\widehat{DBA})=\frac{m(arcAB)}{2}=m(\widehat{C})  =45^{\circ}

    So, m(\widehat{DAB})=m(\widehat{DBA})=45^{\circ}\Right  arrow m(\widehat{ADB})=90^{\circ}
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