But since both the arc and ray have the same points the ray must be bisected as well and the drawing makes no sense, the only way it'll work is if it says DB bisects the ray AC in which case it cuts the 180 degree angle, not the length, in half creating 2 right triangles and my math works. For the record I pasted the picture into paint and in it AE and EC are the same length. I also measured DC and DA and they match. My final answer is that the drawing and info given is an impossibility.
I'll take Paint out of the equation, the figure is probably not drawn to scale. I'd like to ask you one thing- how is it that it can bisect AC. My math isn't the greatest, but I don't recollect studying that property
AC are both points for the arc and the ray if you move one of the points the bisection of the arc changes but the ray changes as well. Draw a circle and run a line through it anywhere then bisect the arc and the ray will be bisected as well since both the arc and ray have the same points.
Try this: Draw a perfect circle then draw a straight line through it. Label the 2 points where the line crosses the circle A and C. Now you have 2 arcs named AC, one running each way so to bisect the arc the bisecting line must run through the middle of the circle thus it'll run through the middle of the line you drew so each part side of the line will be equal. Now the bisecting line of each triangle created is shared thus the same and since you have 2 triangles with 2 sides the same length and each with a 90 degree angle the third side of each triangle must be the same. SO I still believe there is no solution as the info provided is impossible.
This would be my answer: Based on partial info provided EC = 6 but DA and DC must be equal, they can't be 8 and 12 thus with the given info there is no answer. Now if ray DB bisects the angle of ray AC then the answer is 10.77. Either way the drawing is out of whack and I think you teacher is too as there really is no answer and he/she is just screwing with you.
This would be my answer: Based in partial info provided EC = 6 but DA and DC must be equal, they can't be 8 and 12 thus with the given info there is no answer. Now if ray DB bisects the angle of ray AC then the answer is 10.77. Either way the drawing is out of whack and I think you teacher is too as there really is no answer and he/she is just screwing with you. NOTE: No matter where you make points A and C you create a "D" shape and if you bisect any "D" shape the straight line must be 2 equal parts and the bisecting line must form 90 degree angles.
You must have missed an angle.I'm sure in that in the book the problem mentions of an angle.Didn't hear by now of a geopmetry problem like this in wich at least one angle ain't specified. I would ask u the enounce the problem.I'm sure you have missed something
Haha, i have absolutely no idea what the answer is but i have to say this is one of the most precious thread around here....give me stitches...heehee
I agree with you, Roman. The hypotenuse may be 10.77 (I didn't calculate it), but EC should be the same as EA, if bisects means what it usually does. In other words, the only way this would make sense to me is if there were two right triangles of equal size in the drawing.
heh no one solved it yet?? well i see a way to solve it with 3 equations, using cosinuses and sinuses theorems on the 3 emerging triangles, but thats gotta take some time to write
dude..sorry to break it to you, but thats totally wrong. you can use pythagoras only in triangles with a 90 degrees angle and there's nothing that proves that the triangles in here have a 90 degrees angle - which means they dont So you gotta solve it with cosinuses and sinuses theorems and you get 3 equations with 3 variables.. argh thats too much to type
AD would be equal to DC in that case.. which is not true the bisect means angles ADE and EDC are equal, but not the arcs
Your sneezing theories refer to a 3D object, IE ball but the problem clearly states bisecting an arc and here is the definition of an arc: arc (ärk) n. 1. Something shaped like a curve or arch: the vivid arc of a rainbow. 2. Mathematics A segment of a circle. A circle is not a 3D object.
That's the point, the problem is impossible. It clearly states BD bisects arc AC so the arc halves must be equal.
My brain really hurts now. My final answer: Either the info provided is not correct or the teacher game Twan a problem with no solution. I do know one thing: If Twan does not return to this thread when he gets the answer I will red rep him till he does
there you go.. answer is 9 P.S. just noticed gr8liverpoolfan solved it first, so props to him hm.. i think that was my 6,000th post well i guess it was a good one