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Math Help - Circle help

  1. #1
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    Circle help

    Hello! Im glad i found this forums, i need some help. I am stumped on this and have been trying everything, but i seem to be missing something.
    Here is the Question:

    In the picture given PQ is the centreline of circle PWRQ.SP is a touchline of the circle.QWT is a straight line with T on PS



    1. i have to prove that corner P1 = corner P2

    2. I have to prove that SRWT is a koordevierhoek(i dont know what its called in english, but when you have 4 lines in a sircle and they all touch the sides)

    Sorry for not using correct terms but im afrikaans normally.

    Now i have seen that corner w = corner p1 (same circle segment on same basis)

    And that R 2 = 90 degrees

    but from there i am stuck, can someone point me into the right direction and help please?
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  2. #2
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    I do not understand exactly what you mean by corner P1?
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  3. #3
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    I have put the two corners that i have to prove are as big as eachother in red circles, i hope it helps!

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  4. #4
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    Quote Originally Posted by Emeraldswan
    Hello! Im glad i found this forums, i need some help. I am stumped on this and have been trying everything, but i seem to be missing something.
    Here is the Question:

    In the picture given PQ is the centreline of circle PWRQ.SP is a touchline of the circle.QWT is a straight line with T on PS



    1. i have to prove that corner P1 = corner P2
    With the information you have given you cannot show this. You need to tell
    us more, possibly about R or the other angles. All we can say at present is
    that angle PRQ (your R2) is a right angle.

    2. I have to prove that SRWT is a koordevierhoek(i dont know what its called in english, but when you have 4 lines in a sircle and they all touch the sides)
    koordevierhoek - cyclic quadrilateral?


    Sorry for not using correct terms but im afrikaans normally.

    Now i have seen that corner w = corner p1 (same circle segment on same basis)

    And that R 2 = 90 degrees

    but from there i am stuck, can someone point me into the right direction and help please?
    I think you need more information. As described you can move P up and down
    along the tangent, which allows the point R to move on the circle, which will
    change the relative sizes of P1 and P2.

    RonL
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  5. #5
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    Yes, i have to prove that that is a cyclic quadrilateral.

    And as for proving P1 = to P2, i see now that it is unsolvable, i get what you meen by moving P, but can P1 be = to Corner S in anyway then?

    Thanks alot for all the help!
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Emeraldswan
    ... but can P1 be = to Corner S in anyway then?
    Yes, triangle PRQ is similar to triangle SPQ (they are both right triangles and
    angle PQR is common to both), and so P1 and angle PSQ are corresponding
    angles in similar triangles and so equal (congruent).

    RonL
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  7. #7
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    Thanks! i get it! And as for the second one, can you please check if this is correct then.

    Angle W1 + Angle TWR = 180 (Angles on same straight line)

    But P1 = W1 (Triangles on same basis and same circle segment)

    That goes to say that W1 = S

    Wich meens that S + TWR = 180

    thus its a cyclic quadrilateral because opposite sides of cyclic quadrilateral makes 180

    Thanks alot for all the help!!!
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by Emeraldswan
    Thanks! i get it! And as for the second one, can you please check if this is correct then.

    Angle W1 + Angle TWR = 180 (Angles on same straight line)

    But P1 = W1 (Triangles on same basis and same circle segment)

    That goes to say that W1 = S

    Wich meens that S + TWR = 180

    thus its a cyclic quadrilateral because opposite sides of cyclic quadrilateral makes 180

    Thanks alot for all the help!!!
    That looks right to me

    RonL
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