Going in Circles
Bob: ToM Puzzles are not so difficult now a days
Alice: Are you guys able to solve it all
Ted: Except the one when I am too busy
Alice: I have heard that before, you are not busy now
The Circle have three distinct points P,Q, and R. Question is to find another point "S" in the circle so that another circle can be inscribed in the Quadrilateral obtained.
You only have a scale and a compass.
Alice: Are you guys able to solve it all
Ted: Except the one when I am too busy
Alice: I have heard that before, you are not busy now
The Circle have three distinct points P,Q, and R. Question is to find another point "S" in the circle so that another circle can be inscribed in the Quadrilateral obtained.
You only have a scale and a compass.
Labels: friday special, mathemagic
posted by Rajesh Lal at
11:18 AM
18 Comments:
Call me a moron, but won't any fourth point create a quadrilateral in which a circle can be inscribed? If i am wrong than I guess I am just to busy!
Any point S will give a quadrilateral with the other three points.
Any quadrilateral can have a circle inscribed inside it.
Am I missing something?
Chris
i agree. any quadrilateral can have a circle inscribed into it.
POTTER
You might be missing the inscribed part i tried doing this one paper and found that not all points can make quadrilateral with circle "inscribed"
Inscribed = Touching all sides
You cannot do that with just any quadrilateral.
Don't believe me, Try doing that with a rectangle
You cheated if you did it on paper. It says that you only have a scale and a compass, not any paper or anything to right on, let alone a pencil. I would suggest using your "compass" and walking a perfectly sraight line around the earth to make a circle, marking your four points as you go, then start solving from that. Hopefully it doesn't take too many tries, you might get kind of tired. Let me know when you get your answer, I'm curious to know.
it's a compass you use in math not a compass that points north. duh
It's simple. You have the three other points on three of the four legs. To get point s all you have to do is bi-sect the fourth leg.
(P,Q,R,S)=(0,12,240,180)in deg.one an inf. # of solutions
(0,120,240,180)
(0,90,180,270)
I have no idea..
Hey! Don't think I'm dumb, I'm only 12!!
i dont even understand how does a circle have any points?
rofl a circle is made of infinite points... just like any other +1D shape
I think a mathematical "point" is just a position. Anywhere on the circle would be a point. But yah, I couldn't figure it out either.
A way to make a perfect square using a scale and a compass is:
(this is if pt Q is between P and R whereas, if line will be drawn from P to Q, Q to R and R to P, Angle Q will create a 90 degree angle)
first make a line from P to R
then, using a compass, measure Pt. P and Q.
now, using the compass, make an arc below P and R.
note the point that intersects with the perimeter of the circle. that would be pt. S!
to check, place one tip of the compass in pt R. if the other tip intersects with S then it is a perfect square..
(since the question doesnt specify where the points P, Q and R were, Im not sure if this is the answer)
BTW.. the compass here is not the one that points NORTH right??
Its a device use to measure if two seperate lines were equal.
(used on maps, etc..)
I read one comment and passed the one next to it...
how stupid of me..
heheh..
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