+0

# HOLP ME!

0
99
4

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

#1
+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:

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

Mar 23, 2020

#1
+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:

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

heureka Mar 23, 2020
#2
+1

That looks great, thank you!

Guest Mar 23, 2020
#3
+111329
+1

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

CPhill  Mar 23, 2020
#4
+24992
+2

Thank you, CPhill !

heureka  Mar 24, 2020