Geomerty question

[valenzuela]

http://i139.photobucket.com/albums/q307/Valenzuela88/psu2.jpg
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? /images/graemlins/frown.gif

[madnak]

Level?

[valenzuela]

no...but now I know why the blue angle = red + green

[jay_shark]

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 .

[_Z_]

[ 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

[jay_shark]

[ 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 .

[Enrique]

[ 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

[BaldElephant]

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

and

y+r=b

But, I don't know how to get b=g+r

[jay_shark]

[ 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 .

[TWCReborn]

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.

[TWCReborn]

Using the above 2 relationships, you would first show that blue is equal to green+pink and blue is equal to red plus yellow. Thus b = g+p = r+y. To show b = g+r, you must show p = r (can be seen by substitution).

The last part of the puzzle was pointed out above. You can equate red to pink since they subtend the same chord (the lines forming the angles touch the same 2 points on the circle, and thus the vertex, even if you move it around, as long as it is touching the circle will have the same angle).

Plugging in r=p to b=g+p, you get b=g+r.