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Math Help - Circle geometry - too hard for me :(

  1. #1
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    Circle geometry - too hard for me :(

    I have a few questions I don't understand:

    Circle geometry - too hard for me :(-capture-6.png

    I think that x = 60 and y = 60 because somehow x and y are equal. (I don't understand )

    Also:

    If AB and AC are two tangents to a circle and ∠BAC = 116◦, find the magnitudes of the angles in the two segments into which BC divides the circle.

    Could someone draw a diagram and start me off cause I have no idea how the picture works

    Thanks
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  2. #2
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    Yes, x is 60 degrees because the other two angles in the triangle sum to 120 degrees. That means that x subtends and arc in the circle of 2(60)= 120 degrees. If you were to draw the radii from the points where that angle crosses the circle to the center, you would have an angle at the center of the circle of 120 degrees. The angles where those radii meet the tangents from y are, of course, 90 degrees. Thus, you would have a quadrilateral with angles of 90, 90, 120, and y. Since the angles in a quadrilateral add to 360 degrees, you have 90+ 90+ 120+ y= 360 so y= 360- 300= 60 degrees.

    It's hard to believe you don't know what the picture for the second problem looks like. Draw a circle. Mark two points on the circle, B and C. Let A be any point outside the circle and draw lines AB and AC. To find the degree measure of the two arcs (I would NOT say "angles") a similar argument to the first problem works. If you draw the radii from B and C to the center of the circle, you get a quadrilateral in which one angle, the one at A, is 116 degrees and two others, at B and C, are 90 degrees. Again, the sum of angles in a quadrilateral is 360 degrees so x+ 116+ 90+ 90= 360 where x is the measure of the angle at the center of the circle and so the measure of the arc with endpoints B and C. 360 minus that measure is the measure of the other arc.
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  3. #3
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    Hi jgv115,
    Did the original problem want x.y and z?

    bjh
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  4. #4
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    Hey jgv115,

    for the first one, you have :
    a triangle - find x : 180-40-80 = x, therefore x = 60 degrees.

    >> Alternate Segment Theorem :

    the triangle where the angle is 40 degrees yea? to the right is 80 degrees, agreed? (Alternate Segment Theorem)

    on the left of the 40 degrees of the triangle, it would be 60 degrees, agreed?
    (Alternate Segment Theorem)

    put the values in as you go, it will really help.

    if you move the diagram sideways, you'll see another Alternate Segment Theorem, next to the 80 degrees.

    that equals 60 degrees yes?

    therefore, the triangle with pronumeral y, you have 60 + 60 = 120, 180- 120 = 60 degrees.

    therefore y = 60 degrees

    We've established that x = 60, y = 60

    KEEP THE DIAGRAM SIDEWAYS
    Angles on a straight line adds up to 180 degrees.

    Therefore the small angle to the left of 80 degrees will be 180 - 60-80 = 40.

    FLIP your diagram once more, you'll see another ALTERNATE SEGMENT THEOREM.
    the angle on the right of x equals 40 degrees.

    Angles in a triangle add up to 180, so w= 180-40-40 = 100 degrees.

    Lastly, again, angles on a straight line adds up to 180 degrees, x= 60, the angle to the right of x = 40.

    therefore the angle to the left of x = 80 because 180-60-40 = 80 degrees, yes?

    The big triangle, you have found two angles, the one to the right of 40 degrees on the bottom = 80
    the one to the right of x = 80 degrees.

    So you have z= 180 - 80-80= 20 degrees.

    x=60 degrees, y = 60 degrees, w = 100 degrees, z = 20 degrees.

    I'm sorry, it's very hard to explain it, it would be easier if i sat next to you and showed you on a diagram, it would be much easier to understand.
    I tried...

    ------------------------

    Also:

    If AB and AC are two tangents to a circle and ∠BAC = 116◦, find the magnitudes of the angles in the two segments into which BC divides the circle.


    for that one, you have a circle.

    outside of the circle, label point A and from A, draw a tangent to the circle, label B

    at the same time, out side of the circle, from point A, draw a tangent to the circle and label it B.

    The angle made my the two tangents A = 116 degrees.

    Angles B and C will be the same.
    so 180- 116= 64/2 = 32 degrees.

    that's one of the angles.
    and the other one is angles on a straight line.

    180 - 32 = 142 degrees

    so you have the two magnitudes are 32 degrees and 148 degrees.
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