Results 1 to 9 of 9

Math Help - Triangle inscribed in circle

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    114
    Thanks
    1

    Triangle inscribed in circle

    ABC inscribed within a circle whose diameter AC forms one of the sides of hte triangle. If Arc BC on the circle subtends an angle of 40 ddegrees, find the measure of angle BCA within the triangle.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    m\angle ABC = 90^o
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    114
    Thanks
    1
    So ABC is 90 degrees? Then if BAC is 40, BCA would have to be 50? But the answer says BCA is 70.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    How is an inscribed angle measured?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2009
    Posts
    114
    Thanks
    1
    I'm not sure. I haven't done this since high school. Can you explain how to do so?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    m\angle BAC = 20^o
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2009
    Posts
    114
    Thanks
    1
    Isn't it 40? Why is it 20?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    If O is the center of the circle, then

    \angle(BOC) = 40^o

    \angle(BOA) = 180^o - 40^o = 140^o = \angle(OBC) + \angle(OCB)

    But \angle(OBC) = \angle(OCB)

    Now find CBA
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,383
    Thanks
    1318
    You've been given the measure of every angle in the triangle except the one you want!

    An angle with its vertex on a circle subending an arc of \theta degrees has measure \frac{\theta}{2} degrees. Since BC subtends an arc of 40 degrees, angle BAC is 20 degrees. But you asked about angle BCA. There are two ways to get that.

    1) The angles in a triangle sum to 180 degrees. Since AC is a diameter, angle ABC measures 90 degrees. We know that angle BAC is 20 degrees: 180- 90- 20= 180- 110= 70 degrees.

    2) Arc ABC half the circle, 180 degrees. BC measures 40 degrees so arc AB measures 180- 40= 140 degrees. Angle ACB, then, is 140/2= 70 degrees.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. triangle inscribed in a circle...
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 26th 2010, 12:48 PM
  2. Triangle inscribed in one Circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 7th 2010, 07:43 PM
  3. Replies: 2
    Last Post: February 6th 2010, 08:31 AM
  4. triangle inscribed in the circle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 1st 2010, 06:38 AM
  5. Replies: 27
    Last Post: April 27th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum