May 24th, 2013, 02:23 PM  #1 
Newbie Joined: May 2013 Posts: 3 Thanks: 0  Geometry Problem
I'm stuck with these geometry problems Quadrilateral DEFG is inscribed in a circle. ?D = 72 and ?E = 108. Quadrilateral DEFG could be a _______. I. trapezoid II. kite III. rhombus: An airplane is flying north at 625 mph when a wind of 24 mph comes up out of the west. What is the new speed of the plane if no correction is made for the wind? Any help would be appreciated. 
May 24th, 2013, 03:00 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
By using the fact that opposite angles of a cyclic quadrilateral add to 180°, it's easy to show that DEFG is an isosceles trapezoid. For the airplane problem, what effect do you think the wind might have? 
May 24th, 2013, 03:32 PM  #3 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Geometry Problem
For the second problem, it might help to sketch a picture showing the path of the airplane and the direction of the wind, then find the resultant.

May 24th, 2013, 04:07 PM  #4 
Newbie Joined: May 2013 Posts: 3 Thanks: 0  Re: Geometry Problem
I know that the figure must be an isosceles trapezoid but I was confused since it did not have that choice. It only says trapezoid but I guess that isosceles trapezoid is a trapezoid. For the other question I think the wind will make the airplane move a bit northwest. I used the pythagorean theorem and find the resultant and got 625.5 mph. 
May 24th, 2013, 04:30 PM  #5 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Geometry Problem
Yes, that is correct.

May 25th, 2013, 02:04 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
As the wind is from the west, it moves the airplane eastward a bit, but the calculated speed is correct.

May 25th, 2013, 01:40 PM  #7 
Newbie Joined: May 2013 Posts: 3 Thanks: 0  Re: Geometry Problem
yup. my bad. should move northeast a bit 

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