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1.
the angle at the circumference is twice the angle at the centre. so this could be a one or two mark question, potentially more but unlikely, and what they'll do is they'll say "ACD is the centre of the circle. angle ABD is on the circumference. angle ACD is 80 degrees. how big is angle ABD?" or "ABD is 40 degrees, how big is angle ACD?"
2.
angles in the same segment are equal. now i don't 100% understand the wording on that one, but basically it looks like a bowtie (its two lines with diagonals doing from top left to bottom right and top right to bottom left) inside a circle. i can't explain very well, so you might need to search a picture of it, but you'll understand what i mean when you see it. and basically, the two top angles are equal, and the two bottom angles are equal. for this one its best to search an image of it, but i just remember that bowtie = segment
3.
opposite angles in a cyclic quadrilateral add up to 180. a cyclic quadrilateral is a square that is inside a circle, and the opposite angles in it (eg top left and bottom right, or bottom left and top right) are equal. pretty much does what it says in the tin
4.
the angle at the circumference in a semi-circle is always 90. so if you have a point anywhere on the circumference, and it is connected to the diameter, the angle will be 90 degrees
5.
angle between a tangent and a radius is 90 degrees. a tangent is a line that touches the circle in one, and only one, place
6.
two tangents that meet at a point will be equal in length (of distance from their contact point/point they touched the circle)
7.
a radius will always bisect the chord if they cross at 90 degrees. a chord is a line that touches two points inside the circle, but doesn't go through the centre. its like if the diameter just couldnt be bothered. i don't think this is on all exam boards though
8.
the angle between a tangent and a chord is equal to the angle in the alternate segment. this one is a little bit more difficult to explain, but imagine you have a circle with a triangle in it, and lets say the triangle is pointing downwards. the top left angle would be, for example, named a, top right would be b, bottom would be c. if a tangent were to touch the circumference where angle c does, then the angle on the left between the tangent and line AC would equal angle b, and the angle on the right between the tangent and side BC would equal angle a. again it's maybe best to search a picture
1.
the angle at the circumference is twice the angle at the centre. So this could be a one or two mark question, potentially more but unlikely, and what they'll do is they'll say "acd is the centre of the circle. Angle abd is on the circumference. Angle acd is 80 degrees. How big is angle abd?" or "abd is 40 degrees, how big is angle acd?"
2.
angles in the same segment are equal. Now i don't 100% understand the wording on that one, but basically it looks like a bowtie (its two lines with diagonals doing from top left to bottom right and top right to bottom left) inside a circle. I can't explain very well, so you might need to search a picture of it, but you'll understand what i mean when you see it. And basically, the two top angles are equal, and the two bottom angles are equal. For this one its best to search an image of it, but i just remember that bowtie = segment
3.
opposite angles in a cyclic quadrilateral add up to 180. A cyclic quadrilateral is a square that is inside a circle, and the opposite angles in it (eg top left and bottom right, or bottom left and top right) are equal. Pretty much does what it says in the tin
4.
the angle at the circumference in a semi-circle is always 90. So if you have a point anywhere on the circumference, and it is connected to the diameter, the angle will be 90 degrees
5.
angle between a tangent and a radius is 90 degrees. A tangent is a line that touches the circle in one, and only one, place
6.
two tangents that meet at a point will be equal in length (of distance from their contact point/point they touched the circle)
7.
a radius will always bisect the chord if they cross at 90 degrees. A chord is a line that touches two points inside the circle, but doesn't go through the centre. Its like if the diameter just couldnt be bothered. I don't think this is on all exam boards though
8.
the angle between a tangent and a chord is equal to the angle in the alternate segment. This one is a little bit more difficult to explain, but imagine you have a circle with a triangle in it, and lets say the triangle is pointing downwards. The top left angle would be, for example, named a, top right would be b, bottom would be c. If a tangent were to touch the circumference where angle c does, then the angle on the left between the tangent and line ac would equal angle b, and the angle on the right between the tangent and side bc would equal angle a. Again it's maybe best to search a picture
Last reply 2 days ago
went from 3s to 9s with (literally) night before revision - ask me anything59
Last reply 2 days ago
went from 3s to 9s with (literally) night before revision - ask me anything59