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How do you do... (Angles in circles) watch

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    I don't get angles in circles at all... how do you do the question attached, and what are the general rules of angles in circles?

    Edit: How do you do this Rhombus one
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    Angle Y is two times the other angle, so 100 degrees. Sound about right?
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    (Original post by hearthethunder)
    I don't get angles in circles at all... how do you do the question attached, and what are the general rules of angles in circles?
    That's a cyclic quadrilateral... y + 50° = 180°. Same for all cyclic quadrilaterals.

    Another one, hard to explain... You draw a diameter in a circle from A to B. So you have these two points on the circumference, A and B, with the diameter between them. If you draw two lines, from A and B to another point C, then ACB will be 90 degrees.

    Likewise if you have any chord (like a diameter but not through the centre) all the angles made in the same way on one side of it will be the same.

    Now the last one is a tricky one... you'll have to draw it. Imagine a circle with centre O. Now mark any 3 points on the circumference, call them A, B and C. Draw in lines AO, BO, AC and BC. The rule is that AOB = 2ACB. Always. Now on your diagram, imagine moving A, B and C around the circumference into different shapes, some of them look like one triangle inside another, others will be a bit like squares or diamonds etc. The rule is true for all of them as long as you know one of the points is the centre of the circle.
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    Oh no I take it back, that not right. Sorry!!
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    (Original post by thefish_uk)
    That's a cyclic quadrilateral... y + 50° = 180°. Same for all cyclic quadrilaterals.

    Another one, hard to explain... You draw a diameter in a circle from A to B. So you have these two points on the circumference, A and B, with the diameter between them. If you draw two lines, from A and B to another point C, then ACB will be 90 degrees.

    Likewise if you have any chord (like a diameter but not through the centre) all the angles made in the same way on one side of it will be the same.

    Now the last one is a tricky one... you'll have to draw it. Imagine a circle with centre O. Now mark any 3 points on the circumference, call them A, B and C. Draw in lines AO, BO, AC and BC. The rule is that AOB = 2ACB. Always. Now on your diagram, imagine moving A, B and C around the circumference into different shapes, some of them look like one triangle inside another, others will be a bit like squares or diamonds etc. The rule is true for all of them as long as you know one of the points is the centre of the circle.
    Right so 130° then thanks
 
 
 
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