Circle Theorem_11G Part 2

DAE is a tangent to a circle.

Write down the size of angle ABC. Give the reason for your answer

• 61 , alternate segments

• 61 , same segments

• 63, alternate segments

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CCSS.HSG.C.A.2

AC is a tangent to the circle at A and angle AOC = 63°.

Work out the size of angle ACO.

• 63

• 90

• 27

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CCSS.HSG.C.A.2

A, B, C and D lie on a circle centre O.

Angle ABC = 58° and angle CAD = 23°.

Calculate

(a) angle OCA, (b) angle DCA.

• a) 32 b)35

• a)31 b)35

• a)32 b)58

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CCSS.HSG.C.A.2

A, B, C and D are points on the circumference of a circle.Find x, the size of angle ACD. Give a reason for your answer.

• x= 50 same segment

• x=50 . angle in the semicircle is 90

• x=130, cyclic quadrilateral

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CCSS.HSG.C.A.2

A, B and C are three points on the circumference of another circle.O is the centre of the circle.Angle AOB = 112°. Work out the size of angle ACB.

• 224

• 56

• 68

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CCSS.HSG.C.A.2

A, B, C and D are points on the circumference on a circle.Find the size of angle DAB.

• 118

• 62

• 85

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CCSS.HSG.C.A.2

A, B and C are points on the circle, centre O.

AB and OC intersect at P.

Find the value of w.

• 55

• 21

• 73

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CCSS.HSG.C.A.2

The diagram shows the vertices of a triangle lying on the circumference of a circle with centre O.

Find the value of b.

Give a reason for your answer.

• b=90

  angle in a semicircle is 90°

• b=29

  angle in a semicircle is 90°

• b=30

  sum of interior angles of triangle is 180°

Tags

CCSS.HSG.C.A.2

A, B, C and D lie on the circle, centre O, with diameter AC.

PQ is a tangent to the circle at A.

Angle PAD = 60° and angle BAC = 20°.

Find the values of u, v, w, x and y.

• [u = 30.] [v = 60 ] . [w = 60 ], [x = 120,] [y = 40]

• [u = 30.] [v = 20 ] . [w = 50 ], [x = 100,] [y = 30]

Find the size of each lettered angle.

• g=76, h=41, i=76

• g=41, h=76, i=76

• g=41, h=76, i=41

Tags

CCSS.HSG.C.A.2