contestada

A circle passes through the point $A,$ and is tangent to the $y$-axis at the point $B,$ as shown. Find the radius of the circle.

[asy]
unitsize(0.4 cm);

draw((-2,0)--(12,0));
draw((0,-2)--(0,7));
draw(Circle((1.35*pi,2),1.35*pi));

dot("$B = (0,5)$", (0,2), W);
dot("$A = (9,0)$", (8,0), SE);

label("$x$", (12,0), NE);
label("$y$", (0,7), NE);
[/asy]

Respuesta :

Answer:

The radius of the circle is 13

Step-by-step explanation:

[asy]

unitsize(0.4 cm);

draw((-2,0)--(12,0));

draw((0,-2)--(0,7));

draw(Circle((13/2,5),13/2));

dot("B=(0,5)", (0,5), W);

dot("A=(9,0)", (9,0), S);

label("x", (12,0), NE);

label("y", (0,7), NE);

draw((9,0)--(0,5),dashed);

draw((13/2,0)--(13/2,5),dashed);

[/asy]

Since the circle is tangent to the y-axis at B, the center of the circle must lie on a line perpendicular to the y-axis which passes through B.  The only such line which also passes through A is the line AB.  Therefore, the center of the circle is the midpoint of  

AB

.  Since AB has length 9+5=14, the radius of the circle is AB/2=

13

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