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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
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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ash2326Best ResponseYou've already chosen the best response.1
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

ash2326Best ResponseYou've already chosen the best response.1
dw:1358656432945:dw Now angle A= angle C
 one year ago

kryton1212Best ResponseYou've already chosen the best response.1
why they are equal?
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
A= C ( opposite angles of a parallelogram are equal)
 one year ago

kryton1212Best ResponseYou've already chosen the best response.1
isn't that A+C=180?
 one year ago

kryton1212Best ResponseYou've already chosen the best response.1
ohhh. parallelogram .... nothing then continue please
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
For a cyclic quadrilateral opposite angles sum should be 180, we have to satisfy this property also
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
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

ash2326Best ResponseYou've already chosen the best response.1
Therefore a parallelogram with one angle 30 can't be inscribed
 one year ago

kryton1212Best ResponseYou've already chosen the best response.1
ok...how about one angle is 150 degrees? the opp. angle can be 30
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
But opposite angles of a parallelogram are equal,
 one year ago
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