Circle Theorems

Question 1

What is Circle Theorem 1 ?

Clue: Twice

Answer 1

The angle subtended by an arc at the centre is twice the angle subtended by the same arc at the circumference.

Question 2

What is Circle Theorem 2 ?

Clue: Semi-circle

Answer 2

The angle at the circumference of a semi-circle is always a right angle.

Question 3

What is Circle Theorem 3 ?

Clue: Same arc, circumference

Answer 3

The angles at the circumference subtended by the same arc are equal.

Question 4

What is a cyclic quadrilateral ?

Answer 4

A quadrilateral drawn inside of a circle where every vertex of the quadrilateral must touch the circumference of the circle.

Question 5

What is Circle Theorem 4 ?

Clue: Cyclic

Answer 5

The opposite angles in a cyclic quadrilateral add up to 180 degrees.

Question 6

What is Circle Theorem 5 ?

Clue: Tangents

Answer 6

Tangents which meet at the same external point are equal in length.

Question 7

What is Circle Theorem 6 ?

Clue: Centre, chord

Answer 7

A line from the centre of the circle that is perpendicular to a chord bisects the chord ( splits it exactly in half ).

Question 8

What is Circle Theorem 7 ?

Clue: Alternate

Answer 8

The angle between a tangent and a chord is equal to the angle at the circumference subtended by the same chord in the alternate segment.