anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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ash2326
  • ash2326
We start with assuming that the parallelogram is inscribed in a circle. |dw:1358656384414:dw| Assume this to be a parallelogram ABCD
anonymous
  • anonymous
yes
ash2326
  • ash2326
|dw:1358656432945:dw| Now angle A= angle C

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anonymous
  • anonymous
why they are equal?
ash2326
  • ash2326
A= C ( opposite angles of a parallelogram are equal)
anonymous
  • anonymous
isn't that A+C=180?
anonymous
  • anonymous
ohhh. parallelogram .... nothing then continue please
ash2326
  • ash2326
For a cyclic quadrilateral opposite angles sum should be 180, we have to satisfy this property also
anonymous
  • anonymous
ok...
ash2326
  • ash2326
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
anonymous
  • anonymous
and then>
ash2326
  • ash2326
Therefore a parallelogram with one angle 30 can't be inscribed
anonymous
  • anonymous
ok...how about one angle is 150 degrees? the opp. angle can be 30
ash2326
  • ash2326
But opposite angles of a parallelogram are equal,
anonymous
  • anonymous
ohhh yes..
anonymous
  • anonymous
thank you so much
ash2326
  • ash2326
Welcome :D

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