i'm just workin on my algebra and discrete geometry homework, and I'm having trouble with the following question:
I'm totally lost as to where to start. If anyone could post a few pointers to get me started, I'd appreciate it.Triangle ABC is obtuse-angled at C. The bisectors of the exterior angles at A and B meet BC and AC extended at D and E, respectively. If AB = AD = BE, prove that the angle of ACB is 108 degrees.
Naturally I didn't feel inspired enough to read all the links for you, since I already slaved away for long hours under a blistering sun pressing the search button after typing four whole words! - Quzah
You. Fetch me my copy of the Wall Street Journal. You two, fight to the death - Stewie
There is a formula (don't know the proper english name for it) that says:
a^2 = b^2 + c^2 - 2*b*c*cos(A)
where a, b & c are the length's of the trinagle's sides, and A is the angle at the opposite side of side a. Implement this in your figure (see below).
You get:
X^2 = (2Y)^2 + (2Y)^2 - 2*(2Y)*(2Y)*cos(a)
=>
X^2 = 8Y^2 - 8Y^2 * cos(a)
=>
X^2 = 8Y^2 * (1 - cos(a))
=>
(X^2)/(8Y^2) = 1 - cos(a)
=>
cos(a) = 1 - (X^2)/(8Y^2)
=>
a = arccos(1 - (X^2)/(8Y^2))
=>
a = arccos(1 - (1/8)*(X/Y)^2)
Now, the problem is to find some kind of relation between X and Y, but I leave that to you.
Last edited by Magos; 09-04-2003 at 03:52 PM.
MagosX.com
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that's the cosine law
The bisectors of the exterior angles at A and B meet BC and AC extended at D and E, respectively.
Naturally I didn't feel inspired enough to read all the links for you, since I already slaved away for long hours under a blistering sun pressing the search button after typing four whole words! - Quzah
You. Fetch me my copy of the Wall Street Journal. You two, fight to the death - Stewie
That's what caught me up and why i didn't even attempt to answer
what is a bisector of any angle?
A bisector divides the angle in half.
Naturally I didn't feel inspired enough to read all the links for you, since I already slaved away for long hours under a blistering sun pressing the search button after typing four whole words! - Quzah
You. Fetch me my copy of the Wall Street Journal. You two, fight to the death - Stewie
hence the word bisect
bi-sect
To divide into two equal or congruent pieces
the line that bisects the exterior angle should be that same one that bisects the interior angle. Either im missing some thing in the question or Magos is correct in his diagram.Originally posted by XSquared
The bisectors of the exterior angles at A and B meet BC and AC extended at D and E, respectively.
So AB == AD == BE, could that mean angle CAB == ABC? Then ACB + 2CAB = 180 ?
Ok just rambling...
"Think not but that I know these things; or think
I know them not: not therefore am I short
Of knowing what I ought."
-John Milton, Paradise Regained (1671)
"Work hard and it might happen."
-XSquared
This is how I interpreted the question:
Naturally I didn't feel inspired enough to read all the links for you, since I already slaved away for long hours under a blistering sun pressing the search button after typing four whole words! - Quzah
You. Fetch me my copy of the Wall Street Journal. You two, fight to the death - Stewie
