Circle Theorem (Credit to Maths Kitchen for the information)

Question 1

What is an arc?

Answer 1

An arc is part of the circumference of a circle.

Question 2

What is a chord?

Answer 2

A chord is a straight line that connects two points on the circumference. A chord creates two segments.

Question 3

What is a segment?

Answer 3

A segment is part of the circle separated by a chord.

Question 4

What is a subtended angle?

Answer 4

A subtended angle is an angle that ‘comes off’ either end of an arc. (“The angle subtended at the circumference by an arc.”)

Question 5

The angle at the centre is ____ the angle at the ____.

Answer 5

The angle at the centre is double the angle at the circumference.

Question 6

Angles in the same segment are ____.

Answer 6

Any angle subtended from the same two points will always be the same size, as long as they are in the same segment of the circle.

Question 7

Angles subtended from two ends of a semicircle are always ____.

Answer 7

Angles subtended from two ends of a semicircle are always right-angles.

Question 8

What is a cyclic quadrilateral?

Answer 8

In a cyclic quadrilateral, all 4 vertices (corners) must be touching the circumference of the circle.

Question 9

Opposite angles angles in a cyclic quadrilateral always ____ to ____.

Answer 9

Opposite angles in a cyclic quadrilateral always sum (add) to 180 degrees.

Question 10

What is a tangent?

Answer 10

A tangent is a line touching the circumference of a circle, which is always perpendicular to the radius at the point of contact.

Question 11

Tangents that meet a point are equal in ____.

Answer 11

Tangents that meet at a point are equal in length.

Question 12

The angle between a tangent and a chord is equal to which angle?

Answer 12

The angle between a tangent and a chord is equal to the angle in the alternate segment. (Simplified: The angle on the inside of the triangle is equal to the angle opposite and on the outside.

Question 13

How do you identify an isosceles triangle in a circle?

Answer 13

A triangle with two sides that come from the centre of the circle to the circumference, the triangle is isosceles.

Question 14

Where can I practise these theorems?

Answer 14

https://mathskitchen.com/questions/skill/Ge029?qid=Aqa_June2017_2H_12&q=1&nQD=6 :]

Question 15

Where can I find more help on circle theorems?

Answer 15

https://www.youtube.com/watch?v=LiDtSmRNdyA