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Math Help - Construction of tangents

  1. #1
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    Question Construction of tangents

    How to construct 2 equal tangents inclined to each other at 60 degrees for a circle of 5 cm .








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    Last edited by ice_syncer; June 9th 2008 at 09:47 AM.
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  2. #2
    A riddle wrapped in an enigma
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    I assume you're using just a compass and straightedge. This seems too simple, and maybe flawed, but here goes. Maybe someone with more construction skills can jump in.

    Step 1. Construct Circle O with desired radius
    Step 2. Locate point P on circle and draw OP and extend past the circle
    Step 3. Construct a perpendicular at P and extend (Remember the tangent is perpendicular to the radius at the point of tangency)
    Step 4. Construct a segment PR congruent to PO forming equilateral triangle POR (each angle is 60 deg)
    Step 5. Construct OR and extend intersecting tangent line at X.
    Triangle POX is a 30-60-90 right triangle.
    Step 6. Duplicate the 30 deg angle at X and extend to intersect circle at Y, which is the other point of tangency from X

    XP = XY and they are 60 deg apart.

    Pardon my crude drawing.
    Attached Thumbnails Attached Thumbnails Construction of tangents-tangent.jpg  
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  3. #3
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    Quote Originally Posted by masters View Post
    I assume you're using just a compass and straightedge. This seems too simple, and maybe flawed, but here goes. Maybe someone with more construction skills can jump in.

    Step 1. Construct Circle O with desired radius
    Step 2. Locate point P on circle and draw OP and extend past the circle
    Step 3. Construct a perpendicular at P and extend (Remember the tangent is perpendicular to the radius at the point of tangency)
    Step 4. Construct a segment PR congruent to PO forming equilateral triangle POR (each angle is 60 deg)
    Step 5. Construct OR and extend intersecting tangent line at X.
    Triangle POX is a 30-60-90 right triangle.
    Step 6. Duplicate the 30 deg angle at X and extend to intersect circle at Y, which is the other point of tangency from X

    XP = XY and they are 60 deg apart.

    Pardon my crude drawing.

    well, good one but too late, but it's a better method actually...
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