Common Core HSG.C.A.2 worksheet
High school · 16 questions · Common Core: HSG.C.A.2, HSG.C.A.3, HSG.C.A.4 · England: GCSE Higher Geometry
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Question 1
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 34°, and ∠ABC = 47°. Find ∠BAC.
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Question 2
O is the centre of the circle. Which theorem justifies this step? PA = PB, where PA and PB touch the circle
- A. Angles in the same segment are equal
- B. Tangents from an outside point are equal in length
- C. The angle in a semicircle is 90°
- D. Opposite angles of a cyclic quadrilateral add up to 180°
Question 3
O is the centre. ∠AOB = 116° and C is on the major arc. Find ∠ACB.
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Question 4
A tangent from P touches a circle with centre O at T. The radius is 8 cm and OP = 17 cm. Find the length PT.
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Question 5
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 69°. Find ∠AOB.
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Question 6
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 95°. Find ∠AOB.
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Question 7
A tangent touches a circle at A. Chord AB makes an angle of 52° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 8
AB is a diameter of a circle and C is a point on the circle. ∠CAB = 70°. Find ∠CBA.
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Question 9
Two angles at the circumference stand on the same arc. One is 41°. What is the other?
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Question 10
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (2x + 67) cm and PB = (6x + 19) cm. Find x.
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Question 11
ABCD is a cyclic quadrilateral. Angle A = 81°. What is angle C?
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Question 12
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 59°, and ∠ABC = 51°. Find ∠BAC.
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Question 13
O is the centre of the circle. Which theorem justifies this step? ∠AOB = 2 × ∠ACB
- A. The angle at the centre is twice the angle at the circumference
- B. A tangent is perpendicular to the radius
- C. The angle in a semicircle is 90°
- D. Angles in the same segment are equal
Question 14
O is the centre. ∠AOB = 144° and C is on the major arc. Find ∠ACB.
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Question 15
A tangent from P touches a circle with centre O at T. The radius is 5 cm and OP = 13 cm. Find the length PT.
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Question 16
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 47°. Find ∠AOB.
Answer
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