circle theorems

Question 1

angles on same arc / segment theorem

Answer 1

triangles drawn from the same chord will have the same angle when touching the circumference of the circle

Question 2

cyclic quadrilateral theorem

Answer 2

• opposite angles in cyclic quadrilateral add up to 180
• cyclic quadrilateral is a 4 sided shape with every corner touching the circumference of the circle

Question 3

angle at center theorem

Answer 3

the angle at the centre is twice the angle at the circumference

Question 4

chord bisector theorem

Answer 4

a line perpendicular and in the center of a chord will always pass through the centre of the circle

Question 5

tangent and radius perpendicular theorem

Answer 5

the radius will always meet a tangent to the circle at 90

Question 6

tangent from same external point theorem

Answer 6

two tangents drawn from the same outside point are always equal in length

Question 7

angle in a semi circle theorem

Answer 7

• a triangle drawn with the diameter will always make a 90 angle where it hits the circumference
• the diameter subtends a right angle at the circumference

Question 8

alternate segment theorem

Answer 8

the angle between the tangent and the side of the triangle is equal to the opposite interior angle

Question 9

intersecting chords theorem

Answer 9

If AD and BC are 2 chords intersecting at a point P then PA x PD = PB x PC

Question 10

secant tangent theorem

Answer 10

if P is a point outside a circle and T, A, B are points on the circle such that PT is a tangent and PAB is a secant then PT^2 = PA x PB

Question 11

intersecting secants theorem

Answer 11

two secants which cut at point P satisfy intersecting chords theorem where PA x PD = PB x PC