anemone
Gold Member
MHB
POTW Director
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Points $$P$$ and $$Q$$ are centers of the circles as shown below. Chord $$AB$$ is tangent to the circle with center $$P$$. Given that the line $$PQ$$ is parallel to chord $$AB$$ and $$AB=x$$ units, find the area of the shaded region in yellow.
[TIKZ]
\draw [<->] (0.2,1) -- (5.8, 1);
\begin{scope}
\draw (3,0) circle(3);
\end{scope}
\begin{scope}
\draw (1,0) circle(1);
\end{scope}
\coordinate[label=above: P] (P) at (1,0);
\coordinate[label=above: Q] (Q) at (3,0);
\coordinate[label=left: A] (A) at (0.2,1);
\coordinate[label=right: B] (B) at (5.8,1);
\coordinate[label=above: $x$] (x) at (2.8,1);
\filldraw (1,0) circle (2pt);
\filldraw (3,0) circle (2pt);
\draw[fill=red,fill opacity=0.6] (1,0) circle (1);
\draw[fill=yellow,fill opacity=0.5] (3,0) circle (3);
[/TIKZ]
I am not seeking for help, I just want to share an interesting geometry problem at MHB with the hope our members enjoy it. :)
[TIKZ]
\draw [<->] (0.2,1) -- (5.8, 1);
\begin{scope}
\draw (3,0) circle(3);
\end{scope}
\begin{scope}
\draw (1,0) circle(1);
\end{scope}
\coordinate[label=above: P] (P) at (1,0);
\coordinate[label=above: Q] (Q) at (3,0);
\coordinate[label=left: A] (A) at (0.2,1);
\coordinate[label=right: B] (B) at (5.8,1);
\coordinate[label=above: $x$] (x) at (2.8,1);
\filldraw (1,0) circle (2pt);
\filldraw (3,0) circle (2pt);
\draw[fill=red,fill opacity=0.6] (1,0) circle (1);
\draw[fill=yellow,fill opacity=0.5] (3,0) circle (3);
[/TIKZ]
I am not seeking for help, I just want to share an interesting geometry problem at MHB with the hope our members enjoy it. :)