# The 2019 semicircle question: How to calculate diameter of a circle

## The 2019 Semicircle Question:

Five identical semi-circles are arranged as below, we need to find the diameter of 1 circle.

Solution:

This is clearly a geometry question.

Whenever we are trying to solve a geometry problem, we need to consider the shapes involved.

We know that the semicircles are identical, so the diameter for all circles will be the same.

Let’s assume that the diameter will be $\displaystyle{x}$

So, from this, we can determine that:

\begin{align} &\implies &x + 12 + x + 12 + x = 22 + x + 16 + x + 22 \end{align}

If we solve this, we get:

\begin{align} &\implies &3x + 24 &= 2x + 60\\[2ex] &\implies &3x - 2x &= 60-24\\[2ex] &\implies &x &= 36 \end{align}

That’s how we find out that the diameter of one circle is 36.

This is the easiest way to solve this question. If you want solutions to other difficult PSLE Maths questions, we've solved the 2019 triangle question here.

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