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 […]
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 […]
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 […]
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 notice?
Copy the table […]
Find angles xº and yº.
Click here to download the CYCLIC worksheet.
Click here for the Notes […]
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 […]
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 […]