# Geometry of a Circle [closed]

Four Tangent circles are centered on the x-axis. The radius of circle A is twice the radius of circle O. The radius of circle C is four times the radius of circle O. All circles have integer radii and the point (63,16) is on the circle. What is the equation of circle A?The questionnaire is here on the link

## closed as off-topic by pjs36, астон вілла олоф мэллбэрг, Claude Leibovici, John B, DanielJan 2 '17 at 12:00

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – pjs36, астон вілла олоф мэллбэрг, Claude Leibovici, John B, Daniel
If this question can be reworded to fit the rules in the help center, please edit the question.

• The question is badly written. Presumably you are to assume $O$ is centered at the origin and the point $(63,16)$ is on circle $C$. Neither of these is given. – Ross Millikan Jan 2 '17 at 6:31

The circle $O$ has radius $r$, centered at 0. The circle $A$ has radius $2r$, centered at $r+2r=3r$. The circle $B$ has radius $3r$, centered at $3r+2r+3r=8r$. The circle $C$ has radius $4r$, centered at $8r+3r+4r=15r$. The equation of circle $C$ is then $$(63-15r)^2+16^2=16r^2$$ or $$209r^2-1890r+4225=0$$ Only one solution is integer, $r=5$. Then the radius of the circle $A$ is 10, and the equation is $$(x-15)^2+y^2=100$$
If the circle $O$ is centered at the origin with radius $r$, the center of $C$ is $(41r,0)$ and its radius is $24r$, so you need $(63-41r)^2+16^2=(24r)^2$ This is a quadratic, but the solution are a mess. We get $r=\frac {2583 \pm8 \sqrt{31301}}{1105}$ with $A$ centered at $(3r,0)$ and having equation $(x-3r)^2+y^2=4r^2$.Both solutions appear acceptable.