Results 1 to 10 of 10

Math Help - Finding measures inside of a circle?

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    4

    Finding measures inside of a circle?

    Here are a couple of my homework problems that I need some help with. I don't know where to even start. Would someone please be kind enough as to help?

    Problem 1. http://i42.tinypic.com/2ikusjn.jpg
    I need to find measures of angles
    (a) BAC
    (b) ABD
    (c) DBC
    I was also suppose to find measure of arc AD and I found it to be 56, is that correct?

    Problem 2. http://i43.tinypic.com/1fu0xi.jpg
    Solve for x and y.
    I found x = 50 but i have no idea where to start with y.

    Problem 3. http://i44.tinypic.com/34zbubm.jpg
    Solve for z.




    I guess my biggest problem is i don't know the relation between the different inscribed angles. Any help would be greatly appreciated! Thank you very much in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,657
    Thanks
    598

    Re: Finding measures inside of a circle?

    Hello, Hthornton!

    Problem 1. http://i42.tinypic.com/2ikusjn.jpg
    I need to find measures of angles: .(a) BAC . (b) ABD . (c) DBC

    I was also suppose to find measure of arc AD
    . . and I found it to be 56, is that correct? . Yes!

    Theorem: An inscribed angle is measured by one-half its intercepted arc.

    \angle B\!EC = 90^o \quad\Rightarrow\quad \overarc{BC}\,= 90^o \quad\Rightarrow\quad \angle B\!AC = 45^o


    \angle C\!AD = 62^o \quad\Rightarrow\quad \overarc{CD} = 124^o

    \overarc{AD} \:=\:360^o - 90^o - 90^o - 124^o \:=\:56^o

    \angle AB\!D = 28^o


    \overarc{CD} = 124^o \quad\Rightarrow\quad \angle DBC = 62^o
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    4

    Re: Finding measures inside of a circle?

    Thank you very much for your help, Soroban!

    Hthornton
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    4

    Re: Finding measures inside of a circle?

    Would anybody be able to help me with the other two problems?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1

    Re: Finding measures inside of a circle?

    Quote Originally Posted by Hthornton View Post
    Here are a couple of my homework problems that I need some help with. I don't know where to even start. Would someone please be kind enough as to help?


    Problem 2. http://i43.tinypic.com/1fu0xi.jpg
    Solve for x and y.
    I found x = 50 but i have no idea where to start with y.


    I guess my biggest problem is i don't know the relation between the different inscribed angles. Any help would be greatly appreciated! Thank you very much in advance.
    Hi Hthornton,

    Problem 2:

    Angle x is equal to one-half the sum of its subtended arcs. So \angle x = \frac{1}{2}(70+30) = 50

    Angle y is supplementary to angle x. They make up what is called a 'linear pair' and linear pairs are supplementary.

    Problem 3:

    You use the same rule as we did in problem 2. This time find the angle that is supplementary to 124 degees. That would be 180 - 124 = 56 degrees.

    Now apply the same rule as in problem 2. 56=\frac{1}{2}(40+z)
    Last edited by masters; April 3rd 2012 at 10:58 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    4

    Re: Finding measures inside of a circle?

    Thank you kindly!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    903
    Thanks
    27

    Re: Finding measures inside of a circle?

    How can these calculations be performed unless AC is specified adiameter
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1

    Re: Finding measures inside of a circle?

    Quote Originally Posted by bjhopper View Post
    How can these calculations be performed unless AC is specified a diameter
    You wouldn't need the diameter. These are theorems used when two chords intersect inside the circle and subtend arcs on the circle. The chords do not have to be diameters.

    When two chords intersect on the circle, the inscribed angle formed = 1/2 the measure of its subtended arc.

    When two chords intersect inside the circle, each vertical angle formed = 1/2 the sum of the measures of their subtended arcs.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    903
    Thanks
    27

    Re: Finding measures inside of a circle?

    Hello Masters,,
    My comment applies only to problem 1. Tell me about that one.
    Last edited by bjhopper; April 11th 2012 at 11:15 AM. Reason: missing letter
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1

    Re: Finding measures inside of a circle?

    Quote Originally Posted by bjhopper View Post
    Hello Masters,,
    My comment applies only to problem 1. Tell me about that one.
    I see what you mean. It looks like point E is the center and AC passes through E, but that's an assumption. It should have been explicitly stated.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: February 18th 2011, 12:48 PM
  2. Area inside cardioid and also inside circle??
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 19th 2010, 05:57 PM
  3. Replies: 2
    Last Post: October 9th 2008, 04:48 PM
  4. Finding if point is inside or outside of a circle?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 16th 2008, 07:06 PM
  5. Circle Measures!
    Posted in the Geometry Forum
    Replies: 8
    Last Post: May 11th 2007, 05:05 PM

Search Tags


/mathhelpforum @mathhelpforum