Twitter Geometry Puzzle By UK Maths Teacher 🕊
Can You Solve It?
In today’s entry, we will solve a geometry puzzle by UK maths teacher Catriona Agg!
Give this problem a try before jumping in for the solution!
Solution
To start off, we will label the radius of the circle r. Careful observation allows us to show that the width of the rectangle is 3 + 2r.
Consider the pair of similar triangles highlighted below
Both of them are right-angled triangles. We have labelled one of the missing lengths of the green triangle S.
Using Pythagoras Theorem, we find that
The following diagram shows the way the two triangles are similar.
Using properties of similar triangles, we can say that
Now that we know the radius is 1.5, let's label our diagram as such.
The missing part of the height is now x.
To find x, we can consider the purple and yellow triangles. By now, we should be able to see that they are similar.
Therefore, x is
Back to our diagram, we have
The area is therefore
Well done!
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Happy reading,
Barry 🍩