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kryton1212

  • 2 years ago

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.

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  1. ash2326
    • 2 years ago
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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

  2. kryton1212
    • 2 years ago
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    yes

  3. ash2326
    • 2 years ago
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    |dw:1358656432945:dw| Now angle A= angle C

  4. kryton1212
    • 2 years ago
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    why they are equal?

  5. ash2326
    • 2 years ago
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    A= C ( opposite angles of a parallelogram are equal)

  6. kryton1212
    • 2 years ago
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    isn't that A+C=180?

  7. kryton1212
    • 2 years ago
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    ohhh. parallelogram .... nothing then continue please

  8. ash2326
    • 2 years ago
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    For a cyclic quadrilateral opposite angles sum should be 180, we have to satisfy this property also

  9. kryton1212
    • 2 years ago
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    ok...

  10. ash2326
    • 2 years ago
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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

  11. kryton1212
    • 2 years ago
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    and then>

  12. ash2326
    • 2 years ago
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    Therefore a parallelogram with one angle 30 can't be inscribed

  13. kryton1212
    • 2 years ago
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    ok...how about one angle is 150 degrees? the opp. angle can be 30

  14. ash2326
    • 2 years ago
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    But opposite angles of a parallelogram are equal,

  15. kryton1212
    • 2 years ago
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    ohhh yes..

  16. kryton1212
    • 2 years ago
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    thank you so much

  17. ash2326
    • 2 years ago
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    Welcome :D

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