eRevision

Circle Properties & Theorems

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Your Turn!!

Read the above theorem carefully 3 times. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Sketch a copy of Fig. 1 above, drawing first angle ACB then angle AOB. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Sketch the diagram again but this time with B lowered downwards so that it is below A. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Sketch the diagram again but this time with A raised upwards so that it is above B. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Repeat question 2 a few times; this will give you a feel for the theorem, help you remember the theorem and recognise it in examination diagrams. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π

Get it right on the first attempt to mark it as done.

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Your Turn!!

Read this theorem carefully 3 times. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Sketch a copy of the diagram; sketch a circle, then a diameter, then mark any point on the circumference and connect to make a right-angle.
Repeat a few times with different diameters and points. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π

Get it right on the first attempt to mark it as done.

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Your Turn!!

Read this theorem carefully 3 times. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Sketch a circle, draw any chord, and mark any two points on the circumference – on the same side of the chord – then connect the chord to each of the points, making two angles that are equal.
Repeat a few times with different chords and points. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π

Get it right on the first attempt to mark it as done.

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Your Turn!!

Read this theorem carefully 3 times. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Draw any cyclic quadrilateral and mark a pair of angles that sum to 180°. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π

Get it right on the first attempt to mark it as done.

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Your Turn!!

Read this theorem carefully 3 times. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π
Sketch a circle and mark a point on the circumference. From this point, draw a tangent and a chord so the tangent and chord make an angle of above 30°.
Draw the alternate segment and mark the two equal angles. If you have successfully done this, type 'yes'. π + − ÷ × < > ≤ ≥ π

Get it right on the first attempt to mark it as done.

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RAPID TEST

a) If angle ABC is 110°, what is angle ADC? π + − ÷ × < > ≤ ≥ π °
b) State which theorem you used to get this answer, giving the roman numeral from above: π + − ÷ × < > ≤ ≥ π
a) Which angle is twice angle ADB? π + − ÷ × < > ≤ ≥ π
b) State which theorem you used to get this answer, giving the roman numeral from above: π + − ÷ × < > ≤ ≥ π
a) i) Which angle is equal to angle ACB? π + − ÷ × < > ≤ ≥ π
ii) State which theorem you used to get this answer, giving the roman numeral from above: π + − ÷ × < > ≤ ≥ π
b) Is this angle acute (less than 90°) or obtuse (>90°, <180°)? π + − ÷ × < > ≤ ≥ π
a) Which two angles are equal to angle TDC? Separate the angles in your answer using a comma with a space after it. π + − ÷ × < > ≤ ≥ π
b) State which theorem you used to get this answer, giving the roman numeral from above: π + − ÷ × < > ≤ ≥ π

Get it right on the first attempt to mark it as done.

Ok, Done It!