Circle theorems

Question 1

Rule 1

Answer 1

The angle in a semicircle is a right angle

Question 2

Rule 2

Answer 2

A tangent to a circle makes a right angle with the radius at that point

Question 3

Rule 3

Answer 3

A triangle formed by two radii is isosceles

Question 4

Rule 4

Answer 4

A diameter bisects a chord at right angles

Question 5

Rule 5

Answer 5

The angle subtended at the centre of a circle is double the angle subtended at the circumference by the same arc.

Question 6

Rule 6

Answer 6

Angles subtended by an arc in the same segment are equal

Question 7

Rule 7

Answer 7

Opposite angles in a cyclic quadrilateral sum 180. a+c =180. b+d=180

Question 8

Rule 8

Answer 8

Two tangents to a circle drawn from a single point outside the circle are the same length, and create congruent right-angles triangles.

Question 9

Rule 9

Answer 9

The angle between a tangent and a chord is equal to the angle subtended from the ends of the chord in the alternate segment.

Question 10

Rule 10

Answer 10

If two chords PQ and RS cross at point T, then PTxQT=RTxST