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Puzzles

13 December

The diagram to the left shows three circles and two triangles. The three circles all meet at one point. The vertices of the smaller red triangle are at the centres of the circles. The lines connecting the vertices of the larger blue triangle to the point where all three circles meet are diameters of the three circles.
The area of the smaller red triangle is 226. What is the area of the larger blue triangle?

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2 December

Carol draws a square with area 62. She then draws the smallest possible circle that this square is contained inside. Next, she draws the smallest possible square that her circle is contained inside. What is the area of her second square?

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19 December

The diagram below shows three squares and five circles. The four smaller circles are all the same size, and the red square's vertices are the centres of these circles.
The area of the blue square is 14 units. What is the area of the red square?

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5 December

28 points are spaced equally around the circumference of a circle. There are 3276 ways to pick three of these points. The three picked points can be connected to form a triangle. Today's number is the number of these triangles that are isosceles.

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2 December

Today's number is the area of the largest dodecagon that it's possible to fit inside a circle with area \(\displaystyle\frac{172\pi}3\).

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Two semicircles

The diagram shows two semicircles.
\(CD\) is a chord of the larger circle and is parallel to \(AB\). The length of \(CD\) is 8m. What is the area of the shaded region (in terms of \(\pi\))?

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1 December

What is area of the largest area rectangle which will fit in a circle of radius 10?

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Squared circle

Each side of a square has a circle drawn on it as diameter. The square is also inscribed in a fifth circle as shown.
Find the ratio of the total area of the shaded crescents to the area of the square.

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