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© T Madas O O O O O O O The Circle Theorems

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© T Madas 1 st Theorem

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

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

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

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© T Madas Finding the Centre of Rotation

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The shapes below have been produced by rotation. Find the centre of rotation Why does it work?

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

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

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

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© T Madas 2 nd Theorem

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

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

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© T Madas 3 rd Theorem

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© T Madas A central angle is twice as large as any inscribed angle which corresponds to the same arc Central Angle Inscribed Angle O

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

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© T Madas 4 th Theorem

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

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5 th Theorem

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

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© T Madas 6 th Theorem

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

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© T Madas 7 th Theorem

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© T Madas O 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]

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8 th Theorem

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© T Madas O segment sector segment

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© T Madas O Alternating Segments

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© T Madas O 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

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Circle Theorem Test

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Circle Theorem Mini Test

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Practice Question 1

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

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© T Madas Practice Question 2

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© T Madas 50° z 100° 50° 30° x y O

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© T Madas Practice Question 3

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© T Madas 70° a b c 20° 70° 20° O

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© T Madas Practice Question 4

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© T Madas 95° n m 55° 85° 40° p 55° O

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© T Madas Practice Question 5

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© T Madas 25° x y Tangent point 65° O

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© T Madas Practice Question 6

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© T Madas 55° s t 110° O

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© T Madas Practice Question 7

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© T Madas u 28° v 56° O

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© T Madas Practice Question 8

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© T Madas 300° h O 60° 30° 150°

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© T Madas Practice Question 9

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© T Madas 130° c 50° 100° O

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© T Madas Practice Question 10

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© T Madas 50° a b 25° O

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© T Madas 50° a b 130° 25° Can you solve this problem without a circle theorem? O

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© T Madas Practice Question 11

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© T Madas 65° x 230° 115° O

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© T Madas Practice Question 12

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© T Madas 100° z 200° O

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© T Madas Practice Question 13

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© T Madas 84° a b O 42° 138°

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© T Madas Practice Question 14

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© T Madas 32° g O f 148° 32° 64° 296°

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© T Madas Practice Question 15

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© T Madas 115° p O q 65° 90° 25°

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© T Madas Practice Question 16

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© T Madas 90° x O 45°

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© T Madas Practice Question 17

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© T Madas 70° p O A B C AB = BC q r 55° 90° 35° 20°

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© T Madas Practice Question 18

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© T Madas 72° u O v 90° 18° 72°

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© T Madas Practice Question 19

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© T Madas 30° a O b c Tangent point 60° 120°

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© T Madas Practice Question 20

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© T Madas O 58° z y x 32° 58°

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© T Madas Practice Question 21

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© T Madas 85° x O 95° 85°

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© T Madas Practice Question 22

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© T Madas 57° t O r 123° 57° Can you think of another reason as to why both these angles are 57° ?

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© T Madas Practice Question 23

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

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© T Madas Practice Question 24

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© T Madas u 45° 160° 155° O 25° 20° 25° 135° v 20°

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© T Madas Practice Question 25

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© T Madas 30° x O 120° 240°

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© T Madas Practice Question 26

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© T Madas 75° O x 30° 60°

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© T Madas Practice Question 27

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© T Madas 72° x O 144° 18°

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© T Madas Practice Question 28

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© T Madas 40° a O b 140° 50°

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© T Madas Practice Question 29

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© T Madas 30° θ O 60° 30°

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© T Madas Practice Question 30

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© T Madas 25° n O 65°

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© T Madas Practice Question 31

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© T Madas O a 22° b c d Tangent point 22° 68° 56° 124° 68° Exam question

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© T Madas

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