Question

what is the maximum number of tangents to a triangle?

Answer 1

@TuringTest , @UnkleRhaukus , @phi , @saifoo.khan , @ash2326

Answer 2

try drawing as many different tangents on this figure as you can

Answer 3

is it 3 ?

Answer 4

What point could you draw to satisfy that?

Answer 5

I count a whole bunch!

Answer 6

@UnkleRhaukus isnt it 3?

Answer 7

Can't you draw an infinite number through each vertex?

Answer 8

@phi y so?

Answer 9

i count three infinite lines

Answer 10

tangents drawn from the vertices would have no direction
the only question I see is if you want to talk about the number of \(different\) tangents, which I do figure to be 3

Answer 11

ya different tangents

Answer 12

you could draw infinite tangents on any line segment technically, but that seems arbitrary

Answer 13

my doubt is why dont we count the tangent at the 3 vertices?

Answer 14

which way would the tangents at the vertices point?

Answer 15

Do we have to consider that the slope of a tangent at a sharp point is undefined?

Answer 16

i am not sure

Answer 17

a triangle is made with three tangents

Answer 18

OK, by definition a tangent results from a limiting process.... so they do not exist at a vertex... (per wikipedia)

Answer 19

so the answer is 3?

Answer 20

@CliffSedge that is basically how I figured it

Answer 21

If it's tangent to the triangle, then they cannot coincide with the sides of the triangle.

Answer 22

@CliffSedge y so?

Answer 23

Doesn't 'tangent' mean touch at only a single point?

Answer 24

@CliffSedge yes , but the tangent to a straight line is the straight line itself!!!

Answer 25

tangent is nothing but a flat approximation of curve!!

Answer 26

hmmm... looks like there can be several definitions depending on if you're using geometry, calculus, or an even more generalized usage.

Answer 27

i see what i need to knw is this :
can we draw tangent at point A?

Answer 28

I was thinking of it as like a line graphthere is only one unique equation of the tangent line to this graph\[y=mx+b\implies y'=m\]so \(y'=m\) is the only tangent line
in the figure of the triangle you get the same effect for each line segment, of which there are three

Answer 29

Here's my reasoning:
1. tangent is defined as touching at only a single point.
2. in calculus, the slope of *the* tangent line at a sharp point is undefined because there is no single/unique tangent line that can be drawn there.
Therefore: infinite tangent lines are possible.

Answer 30

@Turing but that's not the tangent line, that is the slope of the tangent line which is the line itself. You can't draw a line tangent to another line because it would touch at more than one point.

Answer 31

More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f(c)) on the curve and has slope f'(c) where f' is the derivative of f.
-Wikipedia
that does not require the line to only touch the graph at a single point, the slope just has to match that of the graph at that point

Answer 32

i asked this qn in my lecture and answered it as 3 then one of the srtudents asked if its 6 as in fig:

i couldnt justify it was 3

Answer 33

i told the student i will answer it tmrw dats y i asked

Answer 34

considerthe tangent at point P intersects point Q on the graph, but that does not mean the line is not tangent to the graph at P