circle theorems

Question 1

thorem 1
AACETAC

Answer 1

AACETAAC
angle at centre equal to the angle at circumference
link for more information:

https://thirdspacelearning.com/gcse-maths/geometry-and-measure/circle-theorems/#:~:text=Circle%20Theorem%201%3A%20The%20alternate,chord%20in%20the%20alternate%20segment.

Question 2

theorem 2
angles in a semicircle…

Answer 2

angles in a semi-circle is 90
link for more info:

https://thirdspacelearning.com/gcse-maths/geometry-and-measure/circle-theorems/#:~:text=Circle%20Theorem%201%3A%20The%20alternate,chord%20in%20the%20alternate%20segment.

Question 3

theorem 3
Same segment theorem

Answer 3

angles of the same segment are equal
link for more info:

https://thirdspacelearning.com/gcse-maths/geometry-and-measure/circle-theorems/#:~:text=Circle%20Theorem%201%3A%20The%20alternate,chord%20in%20the%20alternate%20segment.

Question 4

theorem 4
cyclic quadrilateral theorem

Answer 4

opposite angles in a cyclic quaderelateral add to 180
link for more info:

https://thirdspacelearning.com/gcse-maths/geometry-and-measure/circle-theorems/#:~:text=Circle%20Theorem%201%3A%20The%20alternate,chord%20in%20the%20alternate%20segment.

Question 5

theorem 5
ast

Answer 5

alternate segment theorem
the angle, a chord and a tangent at the point of contact is equal to the angle in the alternate segment

Question 6

external tangents are…

Answer 6

of equal length

Question 7

2 radii + chord = …

Answer 7

isosceles

Question 8

complementary

Answer 8

angles add up to 90