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Math Help - Circle Geometry - five question

  1. #1
    Junior Member AlvinCY's Avatar
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    Circle Geometry - five question

    Hey guys,

    Any help on these questions would be great, they're the only five I couldn't get my head around out of a set of 32!

    1) P is a midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN.

    2) PQ and RS are common tangents to two intersecting circles. If T is one of the points of intersection of the two circles, prove that the circles through T, P, Q and through T, R, S touch each other.

    3) ABC is a triangle inscribed in a circle. BE and CF are perpendiculars to AC and AB respectively. AP is drawn perpendicular to EF and, when produced meets the circle at Q. Prove that angle ABQ is a right angle.

    4) Draw three circles that intersect the other two. Prove that the three common chords are concurrent.

    5) A right angled triangle ABC with right angle at A circumscribes a circle of radius r. Prove that r = 0.5(c + b - a) where a, b, c are the length measures of the sides of the triangle.

    Thanks guys!
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  2. #2
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    Quote Originally Posted by AlvinCY View Post
    Any help on these questions would be great, they're the only five I couldn't get my head around out of a set of 32!
    1) P is a midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN.
    2) PQ and RS are common tangents to two intersecting circles. If T is one of the points of intersection of the two circles, prove that the circles through T, P, Q and through T, R, S touch each other.
    3) ABC is a triangle inscribed in a circle. BE and CF are perpendiculars to AC and AB respectively. AP is drawn perpendicular to EF and, when produced meets the circle at Q. Prove that angle ABQ is a right angle.
    4) Draw three circles that intersect the other two. Prove that the three common chords are concurrent.
    5) A right angled triangle ABC with right angle at A circumscribes a circle of radius r. Prove that r s= 0.5(c + b - a) where a, b, c are the length measures of the sides of the triangle.
    May I ask you, "why should any one of us simply answer any one of these questions"?
    If you do get a complete answer, will you use it as your own?
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  3. #3
    Junior Member AlvinCY's Avatar
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    Well.

    To be honest, I don't turn to math help form unless I can't do them myself (I do have a maths degree) it's just that sometimes I get stuck on something simple!

    And plus, they're not for me, I'm tutoring a kid, and the textbook doesn't provide solutions, which is why I'm going to the effort of working it out for them...

    However, I can understand if you choose not to answer any of them!
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  4. #4
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    Quote Originally Posted by AlvinCY View Post
    they're not for me, I'm tutoring a kid, and the textbook doesn't provide solutions, which is why I'm going to the effort of working it out for them...
    Let me see if I really understand this?
    You are being paid as a tutor. You do not understand the subject matter.
    So you ask us to bail you out?
    Last edited by mr fantastic; August 24th 2009 at 06:57 PM. Reason: Shortened the last sentence.
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  5. #5
    Junior Member AlvinCY's Avatar
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    I understand the subject matter, but at times I do get stuck on questions. It's not as if I haven't attempted myself. If you do not wish to answer the questions, then fine.

    This forum is not restricted to students, and therefore as a tutor, I am still able to post questions.

    Anyway, if you wish to delete my thread, then go ahead. But I think that would just be rude and void of the forum's purpose.
    Last edited by mr fantastic; August 24th 2009 at 07:04 PM. Reason: Removed some sentences.
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  6. #6
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    I will keep this thread open for now but any further replies, should there be any, must be kept on-topic to the OP.
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