**"Circle geometry"**

## Years 10 – 11: Investigating circle theorems

*By Barrie Barnard On 27 August, 2020 · Leave a Comment*

Activity 1: Finding the centre of the circle

You will need a cut-out paper circle (about 12cm diameter).

Use a circle that does not show the centre. Fold your circle along a diameter. Mark the ends A and B. Now unfold your circle and then fold again along a different diameter and mark the […]

## Years 11 – 12 Kissing Circles

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

Archimedes (287 BC – 212 BC) wrote about problems like this involving touching circles.

The outer circle, centre O, has radius 2 units.

The points O, A, A’, B and C are centres of circles that are tangent to each other where they touch.

It can be shown that OACB is […]

## Year 11 – 12 Applying the Tangent Theorem

*By Barrie Barnard On 20 February, 2020 · Leave a Comment*

Radio and TV stations broadcast from high towers. Their signals are picked up by radios and TV’s in houses within a certain radius. Because the Earth is spherical, these signals do not get picked up beyond the point of contact of the near horizontal tangent line as illustrated in the sketch.

What is the […]

## Years 10 – 12 Circle Inscribed in Quadrilateral

*By Barrie Barnard On 23 October, 2019 · Leave a Comment*

You are going to investigate quadrilaterals that have inscribed circles as shown in the diagram.

Draw a circle with any radius you choose, and then draw 4 tangents making a quadrilateral with the circle inside touching the quadrilateral at 4 points.

Measure the edge lengths of the quadrilateral ABCD.

What do you […]

## Years 11 – 12 Cyclic

*By toni On 20 May, 2018 · Leave a Comment*

The diagram shows a circle centre O with points P, Q, R and S on the circumference. UST is a tangent to the circle. Angle RPS = 44º and angle PSO = 32º.

Find angles xº and yº.

Click here to download the CYCLIC worksheet.

Click here for the Notes […]

## 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 […]

## 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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