# Find the diameter of one circle

• MHB
• anemone
In summary, the given figure consists of five identical semicircles, where the diameter of one circle is to be found. After analyzing the figure, it can be deduced that the diameter is equal to the sum of the gaps between the semicircles, which is 36.
anemone
Gold Member
MHB
POTW Director
Five identical semicircles are arranged as shown. Find the diameter of one circle.
[TIKZ]
\draw (0,0) -- (16.5, 0);
\begin{scope}
\clip (0,0) rectangle (4.5,4.5);
\draw (2.25,0) circle(2.25);
\draw (0,0) -- (4.5,0);
\end{scope}
\begin{scope}
\clip (6,0) rectangle (10.5,4.5);
\draw (8.25,0) circle(2.25);
\draw (6,0) -- (10.5,0);
\end{scope}
\begin{scope}
\clip (12,0) rectangle (16.5,4.5);
\draw (14.25,0) circle(2.25);
\draw (12,0) -- (16.5,0);
\end{scope}
\begin{scope}
\clip (2.75,0) rectangle (7.25,-4.5);
\draw (5,0) circle(2.25);
\draw (2.75,0) -- (7.25,0);
\end{scope}
\begin{scope}
\clip (9.25,0) rectangle (13.75,-4.5);
\draw (11.5,0) circle(2.25);
\draw (9.25,0) -- (13.75,0);
\end{scope}
\draw [<->] (4.5, 0.5) -- (6, 0.5);
\draw [<->] (10.5, 0.5) -- (12, 0.5);
\draw [<->] (0, -0.5) -- (2.75, -0.5);
\draw [<->] (7.25, -0.5) -- (9.25, -0.5);
\draw [<->] (13.75, -0.5) -- (16.5, -0.5);
\coordinate[label=left:12] (A) at (5.5,0.8);
\coordinate[label=left:12] (B) at (11.5,0.8);
\coordinate[label=left:22] (C) at (1.6,-0.8);
\coordinate[label=left:16] (D) at (8.6,-0.8);
\coordinate[label=left:22] (D) at (15.6,-0.8);
[/TIKZ]

As this is a Singapore primary math problem, it is understandable that one can solve it without the use of algebra method (form an equation and solve the equation is what I mean by algebra method). I enjoyed this problem quite a bit, therefore I wanted to post it here to let others to try to solve it without the use of algebra method...:)

I would say that the sums of the gaps are 24 (above) and 60 (below). As there is one more semicircle above, its diameter is equal to the difference 36.

But, I still count that as an algebra method, hehehe...I will let others have a chance to take a stab at it before I post the so called without-algebra solution. Please stay tuned! :)

Hi castor28!

Here is a diagram to illustrate a slightly different approach than castors28's method:

[TIKZ]
\draw (0,0) -- (16.5, 0);
\begin{scope}
\clip (0,0) rectangle (4.5,4.5);
\draw (2.25,0) circle(2.25);
\draw (0,0) -- (4.5,0);
\end{scope}
\begin{scope}
\clip (6,0) rectangle (10.5,4.5);
\draw (8.25,0) circle(2.25);
\draw (6,0) -- (10.5,0);
\end{scope}
\begin{scope}
\clip (12,0) rectangle (16.5,4.5);
\draw (14.25,0) circle(2.25);
\draw (12,0) -- (16.5,0);
\end{scope}
\begin{scope}
\clip (0,0) rectangle (4.5,-4.5);
\draw (2.25,0) circle(2.25);
\draw (0,0) -- (4.5,0);
\end{scope}
\begin{scope}
\clip (12,0) rectangle (16.5,-4.5);
\draw (14.25,0) circle(2.25);
\draw (12,0) -- (16.5,0);
\end{scope}
\draw [<->] (4.5, 0.5) -- (6, 0.5);
\draw [<->] (10.5, 0.5) -- (12, 0.5);
\draw [<->] (4.5, -0.5) -- (6, -0.5);
\draw [<->] (7.25, -0.5) -- (9.25, -0.5);
\draw [<->] (10.5, -0.5) -- (12, -0.5);
\draw [<->] (6, -0.5) -- (7.25, -0.5);
\draw [<->] (9.25, -0.5) -- (10.5, -0.5);
\coordinate[label=left:12] (A) at (5.5,0.8);
\coordinate[label=left:12] (B) at (11.5,0.8);
\coordinate[label=left:12] (C) at (5.5,-0.8);
\coordinate[label=left:16] (D) at (8.6,-0.8);
\coordinate[label=left:12] (D) at (11.5,-0.8);
\coordinate[label=left:10] (E) at (6.9,-0.8);
\coordinate[label=left:10] (F) at (10.1,-0.8);
[/TIKZ]

$\therefore \text{diameter}=10+16+10=36$

## 1. What is the formula for finding the diameter of a circle?

The formula for finding the diameter of a circle is d = 2r, where d represents the diameter and r represents the radius.

## 2. How do I find the diameter of a circle if I only know the circumference?

To find the diameter of a circle if you only know the circumference, you can use the formula d = c / π, where d represents the diameter, c represents the circumference, and π is approximately 3.14.

## 3. Can I use a ruler to measure the diameter of a circle?

No, a ruler is not an accurate tool for measuring the diameter of a circle. You will need to use a compass or a measuring tape to get an accurate measurement.

## 4. Is the diameter of a circle always equal to twice the radius?

Yes, the diameter of a circle is always equal to twice the radius. This is a fundamental property of circles.

## 5. How do I find the diameter of a circle if I only know the area?

To find the diameter of a circle if you only know the area, you can use the formula d = √(4A / π), where d represents the diameter, A represents the area, and π is approximately 3.14.

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