Results 1 to 3 of 3

Math Help - basic circle geometry

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    81

    basic circle geometry

    Hi all,

    \angle OAP = 90^{\circ}, tangent is perpendicular to radius at point of contact

    \angle OAB = \frac{180-152}{2}=14^{\circ}, angle sum of triangle is 180, triangle OAB is isosceles (equal angles opposite equal sides)

    \angle PAB = 90 -14 = 76^{\circ}

    \angle PBA = 180 - 71 - 76 = 33^{\circ}, angle sum triangle is 180

    BUT....

    Angle sum of quadrilateral is 360^{\circ}

    In which case

    \angle PBA = 360 -152 - 90 - 71 = 47^{\circ}



    is this a poorly drawn up question or is the reasoning flawed?

    thanks.
    Attached Thumbnails Attached Thumbnails basic circle geometry-img397.jpg  
    Last edited by sammy28; July 21st 2010 at 12:00 AM. Reason: forgot to add question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by sammy28 View Post
    Hi all,

    \angle OAP = 90^{\circ}, tangent is perpendicular to radius at point of contact

    \angle OAB = \frac{180-152}{2}=14^{\circ}, angle sum of triangle is 180, triangle OAB is isosceles (equal angles opposite equal sides)

    \angle PAB = 90 -14 = 76^{\circ}

    \angle PBA = 180 - 71 - 76 = 33^{\circ}, angle sum triangle is 180

    BUT....

    Angle sum of quadrilateral is 360^{\circ}

    In which case

    \angle PBA = 360 -152 - 90 - 71 = 47^{\circ}



    is this a poorly drawn up question or is the reasoning flawed?

    thanks.
    What you've calculated is the angle indicated in red.

    Subtract the base angle of the isosceles triangle and you'll get your first result.
    Attached Thumbnails Attached Thumbnails basic circle geometry-tri_vs_quad.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    81
    thanks earboth. i should pay more attention
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basic geometry proof
    Posted in the Geometry Forum
    Replies: 1
    Last Post: September 5th 2011, 07:35 AM
  2. Replies: 6
    Last Post: July 8th 2010, 05:39 PM
  3. Circle Geometry: Centre of Circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: July 8th 2010, 06:44 AM
  4. Basic geometry help
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 25th 2010, 02:42 PM
  5. Basic Coordinate Geometry -Help Please!
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 13th 2007, 10:41 PM

Search Tags


/mathhelpforum @mathhelpforum