**"Circles"**

## Years 9 – 12 Surprise Ratios

*By toni On 3 May, 2020 · Leave a Comment*

A circle of radius r and centre O, is inscribed in a triangle with edges of lengths a, b and c.

Find the area and circumference of the circle.

Find the area and the perimeter of the triangle.

What do you notice about the ratios of the two areas and the ratios […]

## Years 7 – 9 Construct with Circles

*By toni On 24 April, 2020 · Leave a Comment*

a. Draw 2 circles with equal radii, intersecting at C, so that each goes through the centre of the other.

b. Draw a third circle of the same radius with centre C.

c. Draw 4 more circles with centres on the circle centre A and passing through A.

This baobab tree in Senegal is reported to be 6000 years old.

Try to estimate the distance around the tree trunk at its base measured in metres.

Does this picture give you an idea how you might use the picture, with your class at school, to work out a better estimate […]

## Years 8 – 12 Elephant Dreaming

*By toni On 3 July, 2019 · Leave a Comment*

Start to explore ideas of Fibonacci numbers and the golden ratio by copying the picture and drawing this spiral. Watch this inspirational video.

Then create your own elephant. The numbers in the centres of the squares give the radii of the quarter circles that you need to draw.

Continue Reading →

## Years 7 – 9 Construct circle and line patterns

*By toni On 18 February, 2018 · Leave a Comment*

The picture shows you how to use a paper clip to draw circles. You just need to open out the paper clip as shown,

Draw a circle and mark 24 points equally spaced around the circumference. To do this, draw a circle and mark the centre, and mark your first point on […]

## Years 10 – 12 Trig Lengths

*By toni On 23 July, 2016 · Leave a Comment*

In the diagram the line OS is perpendicular to the lines OR and PQ.

The line RS is a tangent at P to the circle centre O and radius 1 unit.

Find the lengths OQ, PQ, PS, OS, OR and RP.

If OS and OR lie on the coordinate axes, what are the coordinates […]

## Years 10 – 11 Cola Can

*By toni On 18 February, 2016 · Leave a Comment*

An aluminium can contains 330 ml of cola.

If the can’s diameter is 6 cm what is the can’s height?

Suppose the can’s height is 10 cm, what does the diameter have to be?

Which of these two cans uses the least aluminium?

If you could choose any diameter which dimensions for the can […]

## Years 8 – 12 Not-So-Square Fence

*By toni On 22 March, 2013 · 5 Comments*

A fence is built around a square field.

Suppose another fence is built exactly one metre longer so the path between the two fences is the same width all the way round including at the corners of the field.

How wide would this path be?

Would a mouse be able to run along it? […]

## Years 8 – 12 Belt Around The Earth

*By AA On 22 March, 2013 · 2 Comments*

A wire belt is tied tightly around the Earth at the equator. Suppose the belt is made exactly one metre longer and held around the Earth at the equator so that it is the same distance away from the Earth everywhere. Would a mouse be able to crawl under the new belt? How do […]

## Grades 11 to 12 – Geometric Trig

*By toni On 21 May, 2012 · 7 Comments*

This is a unit circle with a tangent at A.

The angle marked in the diagram is angle a.

Copy the diagram and find all the angles in terms of the angle a.

Find the six line segments in the diagram corresponding to sina, cosa, tana, 1/sina, 1/cosa and 1/tana.

Find the areas of […]

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