O O The Circle Theorems O O O

The perpendicular bisector of a chord passes through the centre of the circle O

Finding the Centre of Rotation © T Madas

The shapes below have been produced by rotation. Find the centre of rotation ©

Inscribed angles which correspond to the same arc are equal Inscribed Angle O ©

Inscribed angles which correspond to the same arc are equal O Does this inscribed

A central angle is twice as large as any inscribed angle which corresponds to

O O Various Forms of the Theorem O O O © T Madas

O An inscribed angle which corresponds to a diameter (or semicircle) is a right

Opposite angles in a cyclic quadrilateral are supplementary O Cyclic Quadrilateral © T Madas

A tangent and a radius drawn at any point on the circumference of the

The intersection of two tangents to a circle is equidistant from their points of

The angle formed by a chord and a tangent at one of its endpoints

n 40° 55° 85° 95° O m 40° p 55° © T Madas

a 25° O 130° 50° b 25° Can you solve this problem without a

O 296° f 64° 32° 148° 32° g 32° © T Madas

Can you think of another reason as to why both these angles are 57°

y 62° x 124° O 56° 62° w 118° z 56° © T Madas

v 20° 155° 25° 135° O 4 u 5° 20° 160° © T Madas

Exam question Tan gen tp oin t a 22° 68° c 124° 56° b

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O O The Circle Theorems O O O © T Madas

1 st Theorem © T Madas

The perpendicular bisector of a chord passes through the centre of the circle O © T Madas

Finding the Centre of Rotation © T Madas

The shapes below have been produced by rotation. Find the centre of rotation © T Madas

nd 2 m e r o The © T Madas

Inscribed angles which correspond to the same arc are equal Inscribed Angle O © T Madas

Inscribed angles which correspond to the same arc are equal O Does this inscribed angle correspond to the same arc? © T Madas

rd 3 Theorem © T Madas

A central angle is twice as large as any inscribed angle which corresponds to the same arc Inscribed Angle O Cen tra l An gle © T Madas

O O Various Forms of the Theorem O O O © T Madas

th 4 Theorem © T Madas

O An inscribed angle which corresponds to a diameter (or semicircle) is a right angle © T Madas

5 th Theorem © T Madas

Opposite angles in a cyclic quadrilateral are supplementary O Cyclic Quadrilateral © T Madas

6 th Theorem © T Madas

A tangent and a radius drawn at any point on the circumference of the circle meet at right angles O Tangent poin t © T Madas

The intersection of two tangents to a circle is equidistant from their points of contact. [Their angle of intersection and the central angle formed by the radii at the points of contact, are supplementary] O © T Madas

th 8 Theorem © T Madas

sector t n e m seg O nt e m seg me nt g se © T Madas

O Alternating Segments © T Madas

The angle formed by a chord and a tangent at one of its endpoints is equal to the inscribed angle corresponding to the same chord in the alternating segment O © T Madas

Circle Theorem Test © T Madas

Circle Theorem Mini Test © T Madas

Practice Question 1 © T Madas

O 30° 150° 30° 45° 15° x 15° © T Madas

Practice Question 2 © T Madas

50° 30° O z 100° y 50° x 30° © T Madas

Practice Question 3 © T Madas

70° c 70° a 20° O 20° b © T Madas

Practice Question 4 © T Madas

n 40° 55° 85° 95° O m 40° p 55° © T Madas

Practice Question 5 © T Madas

x 25° O y 65° Tange nt poi nt © T Madas

Practice Question 6 © T Madas

s 55° O t 110° © T Madas

Practice Question 7 © T Madas

28° u 28° O v 56° © T Madas

Practice Question 8 © T Madas

h 150° 30° 60° O 300° © T Madas

Practice Question 9 © T Madas

130° 50° O c 100° © T Madas

Practice Question 10 © T Madas

a 25° O 50° b 25° © T Madas

Practice Question 23 © T Madas

y 62° x 124° O 56° 62° w 118° z 56° © T Madas

Practice Question 24 © T Madas

v 20° 155° 25° 135° O 4 u 5° 20° 160° © T Madas

Practice Question 25 © T Madas

x 240° O 120° 30° © T Madas

Practice Question 26 © T Madas

30° 75° O 75° x 60° © T Madas

Practice Question 27 © T Madas

72° O 144° 18° x 18° © T Madas

Practice Question 28 © T Madas

40° b 140° O a 50° 40° © T Madas

Practice Question 29 © T Madas

30° O 60° θ 30° © T Madas

Practice Question 30 © T Madas

25° O n 65° © T Madas

Practice Question 31 © T Madas

Exam question Tan gen tp oin t a 22° 68° c 124° 56° b 68° O d 68° oint p t n e Tang © T Madas