Question

how to construct tangent to a circle in 5 steps

http://www.euclidea.xyz/game/#/packs/Iota/level/Tangent

Answer 1

My construction is taking 6 steps :
http://www.mathopenref.com/consttangents.html

but that site says that the best one takes just 5 steps

Answer 2

that site = euclidea.xyz

Answer 3

are there any other cool methods to construct the tangents ?

Answer 4

I think there must be, I'm trying to use vishwesh's 3-step way of constructing a perpendicular somehow as a way to save steps. Hmmm

Answer 5

segment joining the point and the center (1 steps)
perpendicular bisector (3 steps)
circle at the midpoint (1 step)
join the midpoint to an intersection of circle to form tangent (1 step)

i don't see this can be optimized further w/o inventing a new method ...

Answer 6

The standard method is to construct a perpendicular bisector between a point outside a circle and the center of the circle

Answer 7

Yeah. How the hell did the guys who made this game figure out all these weird constructions? Did they look them up or use a computer to brute force them?

Answer 8

Thanks a lot kai for introducing this game to us :D

Answer 9

Hahaha I am just glad the game is letting me play this level even though I haven't unlocked it yet xD

Answer 10

My aim for a strategy is this (you guys might find something I can't):

Start by making the two circles for the perp. bisector. But instead of doing a line from the two points to make the perp. bisector, start a circle at one of those points and finish it at the other point (or any other point) That still leaves you with one extra move before you have to draw the tangent line.

Also, I find it's easier to click that orange button at the top right when looking for stuff since it makes it clearer if something actually works or not. Hmmm

Answer 11

Wow, thats it !

Answer 12

Oh it works...? I was just suggesting some ideas of how I was trying to solve it, I didn't solve it xD

Answer 13

yeah first step is totally unnecessary haha

Answer 14

Oh no wait, looks it didn't accept the solution..

Answer 15

Here's a process for doing the tangent..It sounds like you have the right method, you just need to use the tools in the window to try to combine a step.

So first, you have to connect the two given points.
Then, draw the perpendicular bisector. There is a perpendicular bisector tool, does that count as one step? Then you draw the circle at the midpoint and lastly draw the tangent.

Answer 16

Yeah I think I just completed it using the perpendicular bisector tool
Try using that. Were you using the compass tool previously?

Answer 17

So basically, the tools you should be using, in order, are
1) line tool
2) perpendicular bisector tool
3) circle tool
4) line tool

It's 4 steps

Answer 18

@Miracrown That is 4 steps to get it, but we're talking about the Euclidean construction steps of only using compass and straightedge. So by that counting, the perpendicular bisector tool counts as 3 steps not 1, since you have to use the circle twice and the line once.

So overall, that makes this process take 6 steps.

Answer 19

And we are back :P

Answer 20

An interesting fact about Euclidea... it doesn't create the best solutions ;) From time to time, someone pops up saying that he/she has a better solution and hence the record changes :P

Answer 21

The more and more I get frustrated by this, the more and more I want to create a program to brute force constructions but I fear it might be harder to create such a thing than I suspect haha

Answer 22

you should have not introduced this kai ugh

Answer 23

Ahahahaha you have gone between thanking me to scorning me in the same post lolol

Answer 24

I was being sarcastic then -.-

Answer 25

I'm still trying to figure out how to visualize that perpendicular construction you showed us earlier @vishweshshrimali5 I feel like the moment I attempt to visualize it I forget it. Weird lol

Answer 26

Psssh stop acting like you don't love this game hahaha

Answer 27

not even brother :p

Answer 28

:P And here I am trying to figure out how to make it in 5 steps :P

Answer 29

he created a semicircle angle @Kainui
http://www.mathopenref.com/constperpendray.html

Answer 30

I know how to do it but it's like if someone just showed you how to tie a knot and then you are trying to tie the knot upside down or backwards or something idk, it's not part of my brain in that way that I can just use it haha

Answer 31

Speaking of tangent to circle problems, I can't get this one in less than 4, maybe the two are related?

http://www.euclidea.xyz/game/#/packs/Beta/level/Tangent1