tooter wrote:smokeybear wrote:i used the law of sines, with the 24 from one of the given blue lines.
Your formula for the Radius is incorrect.
It should be +32 since you need the other red line
Radius is half of the circle, you are saying diameter. radius is from the middle to any point on the outside, therefore it is half of the line "c" plus 16 which is a full line from the middle to the outer edge.
ya i noticed that after the looked again, my mistake. thought you were adding c+16 then dividing by 2
??? tooter? I did not understand your equation. can you please explain it a bit? how the heck did you come up with the radius like that? and what's with the 2m at the end?
Now I'm really confused. 24 and 28 both seem to work.... wth?
Perhaps that fits with my previous argument about since it is not to scale.... you can't directly draw lines and angles and assume that they are that length/angle......
I see your logic smokeybear, and it seems to be correct... but I could not find any errors in 24 either...
Help me disprove one of the 2
i just used congruency rules and alternating angles or whatever, because the lines are paralell, to find out that they are 45.
edit: yes, tooter if you could clarify yours a bit i am also confused. thanks!
tooter wrote:this is what I used
I agree with your answer as well
My calcs:
Given the length of a chord, y, and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the circle :
r = y^2/8x + x/2
where y = 48 (2xblue line)
and x = 16 (red line)
then:
r = (2304/128)+ (16/2)
r = 18 + 8
r = 26
jonathanasdf wrote:??? tooter? I did not understand your equation. can you please explain it a bit? how the heck did you come up with the radius like that? and what's with the 2m at the end?
The 2m should be 2*m
i got the formula from a book
but here is a site that explains what this lenny wants. not the same formula but same idea.
http://mathforum.org/library/drmath/view/55037.html
grr... just redrew it. It seems I made a mistake
28 is right,
24 is wrong...
jeez I hate being wrong.
sry smokey I thought you used the other triangle - the one inside the square.
grrr don't believe I didn't see that other triangle.
o well.
I got the avatar already
GO [insert Altador Cup name here]!!! Own [insert TNT staff here]!!
Hmm tooter.... that equation makes sense, and it works great in this question... but yd u get 26?
WAH! 26 or 28? 28 makes as much sense as this....
!!!!! !! ! ! ! ! !! !! ! !! ! !! ! ! ! I JUST GOT ENLIGHTENED!! ! !! !! ! !! ! !!! !
Tooter, you and your equation along with 26 is right. By this time, most people will have already submitted the wrong answers, me along with them, so congratulations on a well earned couple of thousands if not more.
The explaination is simple: The picture is not drawn to scale! smokey for yours to work, when you extend the side of the square, it must JUST intercept with the blue line at the edge. But imagine this: if the square was drawn larger than scale, then, in actual fact, when the extention goes out and will intercept the blue line BEFORE the edge of the circle, and you'll have 2 unknowns. Because you worked from TNT's picture, which I checked not to be to scale, you were led astray by an illusion. Nice try though.
If you had drawn it to scale yourself, you wouldn't have made the mistake. Ironically, you need the radius to draw it yourself. Oh well, theres always next week.
26 is correct IF the red line is an extension of the diagonal of the triangle. However, I don't see how that assumption can be made.
the formula i used does require that the red be an extension of the squares diagonal (meaning the angle between the blue and square is 45 degrees).
and it has to be.
i dont see how both blue lines can be the same length and all 3 lines parallel if it wasn't an extension (aka 45 degrees)
Don't know if this helps, but I got 26.66 for an answer, and rounding it to the nearest cm would be 27
Quote:26 is correct IF the red line is an extension of the diagonal of the triangle. However, I don't see how that assumption can be made.
it wouldn't matter, if it is parallel to the blue lines then when the blue line is extended and a like red is inserted it would still be mid point of the chord and parallel to the chord thus making it the segment height.
As people argued before, if the angles are not 45 degrees, because this is a circle, if all 3 lines are parallel, the blue lines will be different lengths.
try it yourself.
A quick riddle: Why are manhole covers round?
allright... 26, 27, 28... now i'm confused
and for your manhole covers riddle, it is simple logic. round is the only shape that will not fall into the hole onto some poor guy's head; the round manholes do not vary in diameter, like other shapes, square for example, which could easily fall into the hole.
jonathanasdf wrote:As people argued before, if the angles are not 45 degrees, because this is a circle, if all 3 lines are parallel, the blue lines will be different lengths.
The blue lines are parallel. Why is the red line necessarily parallel to the blue lines?
markr wrote:The blue lines are parallel. Why is the red line necessarily parallel to the blue lines?
Refreshing everyone on the riddle:
Quote:In the following diagram, each blue line is 24 centimetres long, and the red line is 16 centimetres long. Assume the shape in the centre of the circle is a perfect square, and it is exactly centred in the circle. Also assume that all three coloured lines are parallel to each other.
jonathanasdf wrote:I see your logic smokeybear, and it seems to be correct... but I could not find any errors in 24 either...
Help me disprove one of the 2
For anyone who was thinking that radius = 24, because the blue lines equal 24, and the radius is longer than the blue lines, the radius must be greater than 24.
jonathanasdf wrote:A quick riddle: Why are manhole covers round?
Because manholes are round. lol
