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MATH / A unit circle has its center at (5,0) and a second circle with a radius of 2 units has its center at (11,0) as shown. A common internal tangent to the circles intersects the x-axis…

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Answer published by the source. Consult the official source to check your work against its answer.

problem

A unit circle has its center at (5,0)(5,0) and a second circle with a radius of 22 units has its center at (11,0)(11,0) as shown. A common internal tangent to the circles intersects the xx-axis at Q(a,0)Q(a,0). What is the value of aa? [asy] draw((-2,0)--(15,0),Arrows); draw((0,-4)--(0,5),Arrows); draw(Circle((5,0),1)); draw(Circle((11,0),2)); dot((5,0)); dot((7,0)); dot((11,0)); label(scale(0.7)*Label("(5,0)",(3,0),S)); label("Q",(7,0),N); label(scale(0.7)*Label("(11,0)",(11,0),S)); label("xx",(15,0),S); label("yy",(0,5),W); draw((1,3.46410162)--(14,-4.04145188),Arrows); [/asy]
Plain-text mathematical notation (without MathML)
A unit circle has its center at (5,0) and a second circle with a radius of 2 units has its center at (11,0) as shown. A common internal tangent to the circles intersects the x-axis at Q(a,0). What is the value of a? [asy]
draw((-2,0)--(15,0),Arrows);
draw((0,-4)--(0,5),Arrows);
draw(Circle((5,0),1));
draw(Circle((11,0),2));
dot((5,0));
dot((7,0));
dot((11,0));
label(scale(0.7)*Label("(5,0)",(3,0),S));
label("Q",(7,0),N);
label(scale(0.7)*Label("(11,0)",(11,0),S));
label("x",(15,0),S);
label("y",(0,5),W);
draw((1,3.46410162)--(14,-4.04145188),Arrows);
[/asy]
Original LaTeX notation
A unit circle has its center at $(5,0)$ and a second circle with a radius of $2$ units has its center at $(11,0)$ as shown. A common internal tangent to the circles intersects the $x$-axis at $Q(a,0)$. What is the value of $a$? [asy]
draw((-2,0)--(15,0),Arrows);
draw((0,-4)--(0,5),Arrows);
draw(Circle((5,0),1));
draw(Circle((11,0),2));
dot((5,0));
dot((7,0));
dot((11,0));
label(scale(0.7)*Label("(5,0)",(3,0),S));
label("Q",(7,0),N);
label(scale(0.7)*Label("(11,0)",(11,0),S));
label("$x$",(15,0),S);
label("$y$",(0,5),W);
draw((1,3.46410162)--(14,-4.04145188),Arrows);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
a50c368b-325f-58d4-a878-fd4c510281ce
task_key
geometry--test--a50c368b-325f-58d4-a878-fd4c510281ce
task_revision_id
1
config / split
geometry / test

Official source

initial import