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Math Help - Hi All! Need help with this question please! Thank you!

  1. #1
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    Hi All! Need help with this question please! Thank you!

    Hi all! Thank you for taking the time to help me!

    I can't seems to start this question. Hope someone can guide me in the right direction, thanks!

    Attached is a picture of the diagram.

    The question is
    Given AD is tangent to the circle at A.
    BCD is a straight line that intersects the tangent at D.
    DHK is the angle bisector of Angle ADC and it cuts AC at H and AB at K.

    a) show that HD * BD = KD * AD
    * meaning multiply/product.
    b) show that triangle AHK is an isosceles triangle.

    Thank you!
    Attached Thumbnails Attached Thumbnails Hi All! Need help with this question please! Thank you!-20130919_192003.jpg  
    Last edited by mynameiscosine; September 19th 2013 at 04:47 AM.
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  2. #2
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    Re: Hi All! Need help with this question please! Thank you!

    The starting point is to see that angle CAD is equal to the angle CBA.
    (It's a basic angle property of a circle.)
    After that it's a routine similar triangles job.
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  3. #3
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    Re: Hi All! Need help with this question please! Thank you!

    Ohhh. I got it now. Thank you so much! I didn't notice it. Thank you!
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  4. #4
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    Re: Hi All! Need help with this question please! Thank you!

    Hi,
    I was busy drawing the attachment and didn't see that BobP had answered your question. Here's my solution anyway:

    Hi All! Need help with this question please! Thank you!-mhfgeometry39.png
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