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kryton1212 Group Title

A student claims that if one of the interior angles of a parallelogram is 30, then it cannot be inscribed in a circle. Do you agree with him? Explain.

  • one year ago
  • one year ago

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  1. ash2326 Group Title
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    We start with assuming that the parallelogram is inscribed in a circle. |dw:1358656384414:dw| Assume this to be a parallelogram ABCD

    • one year ago
  2. kryton1212 Group Title
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    yes

    • one year ago
  3. ash2326 Group Title
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    |dw:1358656432945:dw| Now angle A= angle C

    • one year ago
  4. kryton1212 Group Title
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    why they are equal?

    • one year ago
  5. ash2326 Group Title
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    A= C ( opposite angles of a parallelogram are equal)

    • one year ago
  6. kryton1212 Group Title
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    isn't that A+C=180?

    • one year ago
  7. kryton1212 Group Title
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    ohhh. parallelogram .... nothing then continue please

    • one year ago
  8. ash2326 Group Title
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    For a cyclic quadrilateral opposite angles sum should be 180, we have to satisfy this property also

    • one year ago
  9. kryton1212 Group Title
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    ok...

    • one year ago
  10. ash2326 Group Title
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    so we have to have \[A=C=90\] this makes the parallelogram a rectangle, so any parallelogram which is inscribed in a circle is a rectangle

    • one year ago
  11. kryton1212 Group Title
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    and then>

    • one year ago
  12. ash2326 Group Title
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    Therefore a parallelogram with one angle 30 can't be inscribed

    • one year ago
  13. kryton1212 Group Title
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    ok...how about one angle is 150 degrees? the opp. angle can be 30

    • one year ago
  14. ash2326 Group Title
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    But opposite angles of a parallelogram are equal,

    • one year ago
  15. kryton1212 Group Title
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    ohhh yes..

    • one year ago
  16. kryton1212 Group Title
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    thank you so much

    • one year ago
  17. ash2326 Group Title
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    Welcome :D

    • one year ago
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