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Tangencies - Contenido educativo

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Subido el 22 de abril de 2024 por Publio P.

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we are going to solve the tangencies worksheet let's start with exercise number one so we are 00:00:01
demanded to draw a tangent line to a circumference of radius 27. first we are going to draw a line 00:00:09
in any direction and there is where we are going to measure the radius okay so with a ruler 00:00:17
we are going to measure 27 a clean line in 27 the arrowhead inside let's draw the arrowhead 00:00:25
clean and with the tip ending on 27 exactly okay this is radius 27 00:00:47
27 we erased the rest of the line leaving the mark there and we are going to draw sorry 00:01:01
we are going to draw the line 27 the circumference radius 27 sorry 00:01:19
oh sorry about that okay so once we have that this circumference is a little bit dirty over 00:01:29
there okay my compass is not a very good one okay excuses but um now we are going to place 00:01:50
the tangency point whatever you want okay so we can choose for example tangency point here 00:01:59
an empty circle like that one this is going to be t the tangency point and for solving the 00:02:08
tangency you have to connect o with t that's another radius and the tangent needs to be 00:02:18
perpendicular to that radius so you can place the square like this or the bevel and the other one 00:02:31
like that move it a little bit keeping the right angle and moving it a little bit down so the point 00:02:48
is free and now we can draw the tangent both sides that's a tangent okay we are going to 00:02:59
name this that tangent as line t lowercase and use the perpendicular symbol with a little dot 00:03:12
inside little arc with a little dot inside first is exercise two and we will draw first 00:03:24
30 millimeters radius circumference on center o okay so with the ruler we will measure 00:03:37
30 millimeters like that okay and we draw the circumference okay that the circumference 00:03:44
radius 30 we normally we don't use those lines to name the radius but okay it's clear enough 00:04:04
now we need we are demanded to do an external r18 circumference on r r is this line okay 00:04:17
that's r so we are going to take this intersection point as a tangency point this is t okay and the 00:04:30
right the radius should be or must be 18 so you will measure 18 from t point down so here 18 00:04:44
that point will be the solution to the first part this is going to be o1 and we are going to call 00:04:59
this tangency point t12 so they are named alike so this is radius radius 18 and we are going to draw 00:05:15
the first solution you place the compass on 01 like this okay that's 01 and you draw the solution 00:05:32
this this shouldn't cross each other okay they only contact in one point 00:05:49
this is not clean enough okay and now um on the other part of the exercise we are demanded to 00:05:56
solve an r23 internal circumference on s s is this one okay this line so we are going to measure 00:06:06
23 this maybe naming r30 here wasn't so clever okay so i'm going to erase that i'm going to name 00:06:17
this o2 and this line this point sorry sorry that point is going to be c2 00:06:43
um r30 we are going to name here for example this is going to be a radius you can do this 00:06:58
in any direction too so this is going to be r30 okay and um and now we are going to name this as 00:07:14
r23 okay sorry for the mess here because this is not so clean okay so r23 r30 if you now place 00:07:33
compass on o2 like this and take the radius o2 t2 you will draw an internal sorry internal 00:07:51
tangent circumference like okay excuse me okay sorry about that because i having some problems 00:08:15
with uh with the compass and with the light so you can see here this is really a mess okay this 00:08:31
must not happen never okay so it should be clean like that one okay so from o2 to t2 00:08:41
second solution from o1 to t1 first solution okay remember the measurements be precise 00:08:52
Exercise number three. Tangent circumferences are 18 and 30 to the line on tangency points. Okay. To the line. So the infinite circumferences that could be tangent to this line will have their centers on this perpendicular. 00:09:01
so if you place if you you place the first ruler in a right angle and the second ruler like this 00:09:31
you take this out and you draw the center's line okay so that's a perpendicular line this is a 00:09:40
right angle okay we are going to name the right angle okay sorry about the light again 00:09:49
this is the right angle here and now this is really really easy because we have to measure 00:10:01
18 i'm going to zoom it a little bit so 18 here and 30 on top be precise like always 00:10:12
last set so this is going to be r18 in there r18 in this is going to be 00:10:33
r30 first solution o1 second solution o2 it's true that you could find 00:10:48
two more solutions so you can draw a 18 circle to the other side a 30 circle to the other side 00:11:00
radius but we are going to give one solution one solution is enough okay so great now we are going 00:11:09
to solve it so placing the compass on o2 till the tangency point t we draw the circumference 00:11:17
okay our solution and we do the same with o1 center till point c again 00:11:27
tangency point and we draw the second solution okay if in class you did the other way around 00:11:39
so if you draw the 13 radius below it's okay and the 18 radius on top it's okay okay it's good 00:11:54
enough great and now we are going to solve number four in number four you have to draw 00:12:06
15 and 28 tangent circumferences to both lines so this is an angle okay r and s great so for 00:12:14
for placing these solutions we need first we need to draw um an angle bisector for drawing 00:12:26
an angle bisector you need to we are going to name this point as v okay this is going to be 00:12:37
the vertex of the angle that's b and for drawing the angle bisector you need to draw one radius 00:12:48
from b not too big not not too small okay something like that with any radius not too big 00:13:00
not too small um and we name we name those two points as one and two okay i'm going to zoom it 00:13:12
little bit so with any radius that arc okay you cross both lines and now from one and two you're 00:13:26
going to do two arches okay with any radius again you can change the radius from the first one okay 00:13:38
so we are going to take for example this one any radius again you choose the radius 00:13:48
you do that arc draw that arc and from two you do the same okay again that's from one 00:13:54
with any radius and with the same radius from two so the arches cross each other now we are going to 00:14:05
place exactly sorry for the light to place exactly the crossing point okay and connect 00:14:15
this is going to be named three and we are going to connect i'm going to zoom out v with three 00:14:27
okay and by doing that i'm going to change the ruler by doing that 00:14:40
vm3 you will get the set the the angle sorry bisector okay if you do this and these two parts 00:14:47
doesn't seem equal repeat okay because angle bisector sometimes are tricky okay and now 00:14:59
here on that angle by sector we would have infinite circumferences tangent to the to both 00:15:09
lines but we only need radius 15 and radius 28 tangents so for placing those two solutions we 00:15:17
need to draw parallel lines to draw that parallel lines i'm going to zoom it a little bit 00:15:29
to draw that parallel line we are going to need perpendicular okay so here 00:15:40
perpendicular to S as far as you can go okay so here on S as right as you can go 00:15:58
draw a perpendicular here okay I'm more or less one centimeter apart something 00:16:13
like that one centimeter apart we are going to draw another perpendicular if 00:16:28
you want to do it exactly you can also use this ruler here on line s and this 00:16:38
other one on top okay good so doing that you will get the other perpendicular okay so right 00:16:45
angle here and right angle here on both and now we are going to measure the 28 and the 15 millimeters 00:17:01
on those parallels so 28 and 50 in okay 15 28 now we erase the rest of the line we don't need okay 00:17:12
and we are going to draw arrowheads be clean keep the accuracy and this is r 00:17:41
sorry that's r15 and that's r28 please keep the position of the numbers okay 00:18:09
these are vertical and they always turn to the left okay good and now we are going to draw the 00:18:27
parallels for drawing the parallels you need to place the first ruler on s second ruler 00:18:42
you place is beside the other one okay so beside the other one like this okay something like that 00:18:52
and now i'm going to zoom in again the second one keeps still this one keeps still 00:19:07
and you move it to the measure 15 like that parallel line and you do the same on measure 00:19:15
28 both parallel lines you need the parallel line to cross the d-angle bisector okay that way 00:19:30
where the parallel crosses the angle of a sector you get the solutions o1 and o2 but this is not 00:19:39
solved yet because we need the tangency points to exactly solve this the problem okay for the 00:19:56
tangency points to place you need to do this you are going to draw from perpendicular to line r 00:20:04
passing through o1 right angle okay look at the ruler so right angle 00:20:15
tangency point and you do the same perpendicular to r passing through 00:20:24
0.02 so you have two perpendiculars here and here and you do the same with line s with the 00:20:33
horizontal be careful and don't do this okay this is wrong you need a perpendicular not to the 00:20:48
angle bisector but to the line so we're going to draw perpendicular to the line here and here 00:20:57
okay so you have two perpendiculars there here and here so you have the tangency points 00:21:25
we have the four tangency points okay good and by the way three and no one 00:21:37
doesn't have anything to do okay so maybe in your in your case three is lower than than no one 00:21:49
okay so because you place three wherever you want great so we are finishing now we are going to draw 00:21:58
the solutions so placing the compass on 01 you have the first solution okay again so you place 00:22:06
the compass on 01 and this is the radius till the tangency point and you draw the first solution 00:22:25
so this is the first solution there you have a little mistake okay this should pass through 00:22:37
the tangency point this is a one millimeter mistake okay and we are going to do the same 00:22:49
with o2 so you draw the circumference and the mistake is here again okay why is this mistake 00:22:58
happening because the angle bisector is one millimeter higher than the position it should be 00:23:12
okay it's a very very normal mistake so if it happens to you don't be so worried okay 00:23:19
thank you for listening 00:23:31
Idioma/s:
en
Autor/es:
Publio Pérez Prieto
Subido por:
Publio P.
Licencia:
Reconocimiento - No comercial - Sin obra derivada
Visualizaciones:
107
Fecha:
22 de abril de 2024 - 21:14
Visibilidad:
Público
Centro:
IES PEDRO DUQUE
Duración:
23′ 35″
Relación de aspecto:
1.78:1
Resolución:
1920x1080 píxeles
Tamaño:
3.26

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