Round Trips
"Round Trips" takes you on a quick journey around the ways angles behave when lines and circles are combined. Before we do this you'll need to know some of the special terms which are used to describe parts of a circle. Unfortunately you'll need to know these "jargon" terms as it will certainly be examiner-speak for these type of problems.
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There are just a couple more terms
which you need to know: perpendicular means at
right-angles to and bisector means something which
cuts a sector into two.
If you now learn these properties
in the table below you should be able to answer any questions which involve
circles and lines. Don't worry about the words, make sure that you visualise
what is happening and remember it (the easiest way to do this may be to try
out some practice problems).
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The angle at the centre is twice the angle at the circumference. |
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Angles in the same segment are equal. |
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The angle in a semicircle is always a right-angle. |
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Opposite angles of a cyclic quadrilateral (i.e. all points of the quadrilaterial are on the circumference) add up to 180° (a+c = 180° and b+d = 180°). |
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A tangent meets the radius of a circle at 90° (a right-angle). |
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The angle between a tangent and a chord is equal to the angle in the alternate segment. |
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The perpendicular bisector of any chord passes through the centre of the circle. |
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The lengths of two tangents from a point are equal. |
When you are asked to answer questions on circle properties, you must give reasons explaining why your solution is correct. For example if you say something like angle a = angle b on its own you could be guessing. However, if you say angle a = angle b (angles in the same segment) you'll get the marks you deserve.