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#1
11-30-2007, 02:30 PM
 valenzuela Senior Member Join Date: Dec 2004 Location: Santiago, Chile Posts: 6,508
Geomerty question

The black dot is the centre of the circunference btw.

Is the blue angle equal to the sums of the green angle and the red angle? My textbook says it is but I dont see how can that be? [img]/images/graemlins/frown.gif[/img]
#2
11-30-2007, 02:54 PM
 madnak Senior Member Join Date: Aug 2005 Location: Brooklyn (Red Hook) Posts: 5,271
Re: Geomerty question

Level?
#3
11-30-2007, 03:00 PM
 valenzuela Senior Member Join Date: Dec 2004 Location: Santiago, Chile Posts: 6,508
Re: Geomerty question

no...but now I know why the blue angle = red + green
#4
11-30-2007, 04:09 PM
 jay_shark Senior Member Join Date: Sep 2006 Posts: 2,277
Re: Geomerty question

Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )

So we require to show that the blue angle = the pink angle + the green angle . But this follows from the exterior angles theorem .
#5
11-30-2007, 04:45 PM
 _Z_ Senior Member Join Date: Jul 2004 Posts: 356
Re: Geomerty question

[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )

[/ QUOTE ]

Green and pink are not necessarily equal.

You meant to say:

Angle green = angle yellow since they are subtended by the same chord.

So it is sufficient to show that blue = yellow + red.

Z
#6
11-30-2007, 07:58 PM
 jay_shark Senior Member Join Date: Sep 2006 Posts: 2,277
Re: Geomerty question

[ QUOTE ]
[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )

[/ QUOTE ]

Green and pink are not necessarily equal.

Z

[/ QUOTE ]

I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .
#7
11-30-2007, 08:47 PM
 Enrique Senior Member Join Date: Mar 2005 Location: Mexico Posts: 621
Re: Geomerty question

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )

[/ QUOTE ]

Green and pink are not necessarily equal.

Z

[/ QUOTE ]

I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .

[/ QUOTE ]

You wrote angle green = angle pink.
That statement is false. Although you give the explanation about angle green and angle yellow opening the same chord, hence angle green = angle yellow. And now you can say angle blue = angle yellow + angle red
#8
11-30-2007, 10:44 PM
 BaldElephant Member Join Date: Oct 2007 Posts: 34
Re: Geomerty question

Hmm, it's clear that:
g+p=b

and

y+r=b

But, I don't know how to get b=g+r
#9
11-30-2007, 10:48 PM
 jay_shark Senior Member Join Date: Sep 2006 Posts: 2,277
Re: Geomerty question

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )

[/ QUOTE ]

Green and pink are not necessarily equal.

Z

[/ QUOTE ]

I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .

[/ QUOTE ]

You wrote angle green = angle pink.
That statement is false. Although you give the explanation about angle green and angle yellow opening the same chord, hence angle green = angle yellow. And now you can say angle blue = angle yellow + angle red

[/ QUOTE ]

It was a typo . Thx for clearing that up .
#10
11-30-2007, 10:53 PM
 TWCReborn Junior Member Join Date: Nov 2007 Location: Los Angeles Posts: 16
Re: Geomerty question

These types of problems are very simple. Ignore the circle in the beginning. Two properties are used:
1.) Two angles forming a straight angle are supplementary angles. Basically this means when there are two angles side by side on a straight line, they add up to 180 degrees.
2.) The 3 angles on a triangle add up to 180 degrees.

The rest is just algebra. Label each relevant angle x, y, z, etc. Write out relationships that you find. Combine equations to show your desired equality.

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