+0  
 
0
99
4
avatar

Two unit circles are externally tangent at B. Let AB and BC be diameters of the two circles. A tangent is drawn from A to the circle with diameter BC, and a tangent is drawn from C to the circle with diameter AB, so that the two tangent lines are parallel. Find the distance between the two lines of tangency.

Asymptote Image:[asy]
unitsize(1.5 cm);

pair P, Q, R, T, U;

P = (-2,0);
Q = (0,0);
R = -P;
T = (2/3,2*sqrt(2)/3);
U = -T;

draw(Circle((-1,0),1));
draw(Circle((1,0),1));
draw(P--(T + 0.2*(T - P)));
draw(R--(U + 0.2*(U - R)));

dot("$A$", P, W);
dot("$B$", Q, E);
dot("$C$", R, E);
[/asy]

 Mar 22, 2020

Best Answer 

 #1
avatar+24992 
+2

Two unit circles are externally tangent at B. Let AB and BC be diameters of the two circles.

A tangent is drawn from A to the circle with diameter BC, and a tangent is drawn from C to the circle with diameter AB,

so that the two tangent lines are parallel.

Find the distance between the two lines of tangency.

 

I assume:

\(\begin{array}{|rcll|} \hline \mathbf{\dfrac{x-1}{1}} &=& \mathbf{\dfrac{1}{3}} \\\\ x-1 &=& \dfrac{1}{3} \\ x &=& 1+ \dfrac{1}{3} \\ \mathbf{x} &=& \mathbf{\dfrac{4}{3}} \\ \hline \end{array}\)

 

laugh

 Mar 23, 2020
 #1
avatar+24992 
+2
Best Answer

Two unit circles are externally tangent at B. Let AB and BC be diameters of the two circles.

A tangent is drawn from A to the circle with diameter BC, and a tangent is drawn from C to the circle with diameter AB,

so that the two tangent lines are parallel.

Find the distance between the two lines of tangency.

 

I assume:

\(\begin{array}{|rcll|} \hline \mathbf{\dfrac{x-1}{1}} &=& \mathbf{\dfrac{1}{3}} \\\\ x-1 &=& \dfrac{1}{3} \\ x &=& 1+ \dfrac{1}{3} \\ \mathbf{x} &=& \mathbf{\dfrac{4}{3}} \\ \hline \end{array}\)

 

laugh

heureka Mar 23, 2020
 #2
avatar
+1

That looks great, thank you! smiley

Guest Mar 23, 2020
 #3
avatar+111329 
+1

LOL!!!!!....you made that look too easy, heureka  !!!!

 

 

cool cool cool

CPhill  Mar 23, 2020
 #4
avatar+24992 
+2

Thank you, CPhill !

 

laugh

heureka  Mar 24, 2020

12 Online Users

avatar
avatar