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February 10th, 2010, 11:58 PM   #1
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super hard 16 year old CIRCLE THEOREMS questions please help

hey guys me again,

Doing circle theorems which is to me, super hard

need your help

please show me step by step what you did and how you did it
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February 11th, 2010, 05:18 AM   #2
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1. Let T be a point "below" P on the given tangent.
Angle SQP = angle TPS by the alternate segment theorem
= angle PSQ since TP is parallel to SQ,
so SP = PQ (chords subtending equal angles),
and so angle PRS = angle PRQ (angles subtended by equal chords),
i.e., PR bisects ?QRS.

2a. ?CTD + ?CAD = ?CTD + ?TAC + ?TAD
= ?CTD + ?TCD + ?TDC by the alternate segment theorem
= 180 (angles of a triangle),
so TCAD is a cyclic quadrilateral (opposite angles supplementary).

2b. ?TAC = ?TCD by the alternate segment theorem
= ?TAD (both angles subtended by TD, with TCAD cyclic).

2c. = ?TDC by the alternate segment theorem,
so triangle TCD is isosceles, with TC = TD (equal sides opposite equal angles).
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February 11th, 2010, 11:46 AM   #3
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Re: super hard 16 year old CIRCLE THEOREMS questions please help

Hello, peterle1!

Quote:

Code:
            *           *
          *               *
         *                 o R
                          /
        *                /  *
        *               /   *
      S o - - - - - - -o- - o Q
                      / X
         *           /     *
          *         /     *
            *      /    * 
      T - - - - * o * - - - - U
                  P

Draw chords PQ, QR, RS, and SP.


Quote:







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Parallel lines intercept equal arcs.






Quote:










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