Catriona Shearer's Puzzles

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Catriona's Puzzles

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Catriona's Puzzle Pages


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Find the angle in the triangle in the circle in the triangle in the semi-circle.

1/ Draw two radii from the tangents to the centre of the small circle.

2/ Radii always meet tangents at 90º, also the large triangle in the semi circle has an angle of 90º This means that a square has formed, and so the angle where the radii meet is also 90º

3/ Use the theorem that says: "The angle at the centre of a circle is twice the angle at the circumference". If the centre angle is 90º then our mystery angle must be 45º !

Here are four squares. The area of the little square=5. What's the area of the blue triangle?

1/ Note that both small squares have area =5. The medium square is the size of four small squares so it has area=20. Amazingly, it doesn't matter how big the biggest square is!

2/ The green lines are parallel. Therefore, as the blue and pink triangles have the same base and same height, their areas are equal.

3/ Again, the green lines are parallel, so the blue triangle has the same area as the pink triangle.

4/ The grey triangle is half the 20 square, so the area = 10. This is the same as the original blue triangle!