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Math Help - Circle Geometry

  1. #1
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    Circle Geometry

    Two questions, please. I have provided diagrams!

    1. Find the measurement of <a, <b, <c, and <d. Explain your reasoning in each case.

    http://img.photobucket.com/albums/v1...en/math001.jpg

    2. In the diagram, tangents have been drawn from P to the circles. If O is the center of the smaller circle, find the exact value of PO. Explain your reasoning.

    http://img.photobucket.com/albums/v1...en/math002.jpg

    If you could elaborate on how to come to the answer, that'd be great!
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  2. #2
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    Re: Circle Geometry

    Quote Originally Posted by Momorii View Post
    Two questions, please. I have provided diagrams!

    ...

    2. In the diagram, tangents have been drawn from P to the circles. If O is the center of the smaller circle, find the exact value of PO. Explain your reasoning.

    http://img.photobucket.com/albums/v1...en/math002.jpg

    If you could elaborate on how to come to the answer, that'd be great!
    1. If PB is the common tangent to both circles then

    |\overline{PA}| = |\overline{PB}| = |\overline{PC}|

    2. \Delta POC is a right triangle. Calculate the length of the hypotenuse using Pythagorean theorem.
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  3. #3
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    Re: Circle Geometry

    Quote Originally Posted by Momorii View Post
    Two questions, please. I have provided diagrams!

    1. Find the measurement of <a, <b, <c, and <d. Explain your reasoning in each case.

    http://img.photobucket.com/albums/v1...en/math001.jpg

    2. ...
    1. Have a look here (better look twice!): Inscribed angle - Wikipedia, the free encyclopedia

    2. Using the above mentioned theorem you'll get:

    \angle(a)=102^\circ (btw why?)

    \angle(a) + \angle(d) =180^\circ

    \angle(c) + 51^\circ =90^\circ (btw why?)

    \angle(b) = \frac12 \ \angle(a)
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