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How do I calculate angles where circles are involved?

By Jack Putt on the 11th of June, 2012

2 Answers

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    In your General Level Exam you might have to deal with angles which are features of a circle.

    Important facts about circles

    There are some important facts you have to remember -

    A turquoise circle with a line through its diameter and a dot in the centre.

    A diameter is a line which passes through the centre of a circle.

    A circle with its radius shown in a line and a dot at the centre.

    A radius is a line from the centre of a circle to the circumference.

    A circle, on top of a horizontal line, which is the same length as the circle's diameter.

    A tangent is a line which touches a circle at one point only.

    A circle with a vertical line beside it. Where the edge of the circle meets the middle of the line a right angle is indicated bertween this and the radius line.

    The angle between a tangent and a radius is a right angle of 90°.

    A circle with its diameter marked. The diameter forms the hypotenuse of a right angled triangle going up to the circle's edge. Where the two lines of the trianle meet, a right angle is shown.

    Any angle in a semicircle is a right angle of 90°.

    Refine By Pinaki Panda on the 16th of January, 2013

  • 0
    Vote

    In your General Level Exam you might have to deal with angles which are features of a circle.

    Important facts about circles

    There are some important facts you have to remember -

    A turquoise circle with a line through its diameter and a dot in the centre.

    A diameter is a line which passes through the centre of a circle.

    A circle with its radius shown in a line and a dot at the centre.

    A radius is a line from the centre of a circle to the circumference.

    A circle, on top of a horizontal line, which is the same length as the circle's diameter.

    A tangent is a line which touches a circle at one point only.

    A circle with a vertical line beside it. Where the edge of the circle meets the middle of the line a right angle is indicated bertween this and the radius line.

    The angle between a tangent and a radius is a right angle of 90°.

    A circle with its diameter marked. The diameter forms the hypotenuse of a right angled triangle going up to the circle's edge. Where the two lines of the trianle meet, a right angle is shown.

    Any angle in a semicircle is a right angle of 90°.

    Refine By Pinaki Panda on the 16th of January, 2013

Suggested reading…

Calculate angles where circles are involved

Circle Theorems

1. An angle subtended at the centre, is twice the angle subtended at edge

2. The angle at the edge of semi circle, subtended by the diameter, is always a right angle

3. Opposite angles in a quadrilateral, where all its corners are on the edge of a circle, sum to 180o So in the below example Do = 78o and Co = 63o

4. Angles subtended on the same arc are equal

 

You will need to remember these theorems and be able to recognise them in order to solve problems.

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