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Common Core HSG.C.A.3 worksheet

High school · 16 questions · Common Core: HSG.C.A.2, HSG.C.A.3 · England: GCSE Higher Geometry

Name

Date

Score/ 16

  1. Question 1

    A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 42° and ∠BAC = 47°. Find ∠ACD.

    Answer

  2. Question 2

    Two angles at the circumference stand on the same arc. One is 59°. What is the other?

    Answer

  3. Question 3

    ABCD is a cyclic quadrilateral. Angle A = 106°. What is angle C?

    Answer

  4. Question 4

    In cyclic quadrilateral PQRS, ∠P = (2x − 5)° and ∠R = (3x + 55)°. Find x.

    Answer

  5. Question 5

    ABCD is a cyclic quadrilateral. ∠DAB = 68°. Find ∠BCD.

    Answer

  6. Question 6

    O is the centre of the circle. Which theorem justifies this step? ∠AOB = 2 × ∠ACB

    • A. Tangents from an outside point are equal in length
    • B. The angle at the centre is twice the angle at the circumference
    • C. A tangent is perpendicular to the radius
    • D. The angle in a semicircle is 90°

  7. Question 7

    A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 34° and ∠BAC = 50°. Find ∠ACD.

    Answer

  8. Question 8

    Two angles at the circumference stand on the same arc. One is 55°. What is the other?

    Answer

  9. Question 9

    The angle at the circumference is 51°, standing on the same arc as the angle at the centre. What is the angle at the centre?

    Answer

  10. Question 10

    In cyclic quadrilateral PQRS, ∠P = (4x + 2)° and ∠R = (3x + 52)°. Find x.

    Answer

  11. Question 11

    ABCD is a cyclic quadrilateral. ∠ABC = 75°. Find ∠ADC.

    Answer

  12. Question 12

    O is the centre of the circle. Which theorem justifies this step? PA = PB, where PA and PB touch the circle

    • A. Opposite angles of a cyclic quadrilateral add up to 180°
    • B. The angle in a semicircle is 90°
    • C. Tangents from an outside point are equal in length
    • D. The angle at the centre is twice the angle at the circumference

  13. Question 13

    A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 59° and ∠BAC = 52°. Find ∠ACD.

    Answer

  14. Question 14

    Two angles at the circumference stand on the same arc. One is 65°. What is the other?

    Answer

  15. Question 15

    A triangle is drawn in a semicircle with one side the diameter. One of the other angles is 73°. What is the third angle (not the right angle)?

    Answer

  16. Question 16

    In cyclic quadrilateral PQRS, ∠P = (3x + 9)° and ∠R = (x + 27)°. Find x.

    Answer

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Answer key: Common Core HSG.C.A.3 worksheet

  1. 1. 42

  2. 2. 59

  3. 3. 74

  4. 4. 26

  5. 5. 112

  6. 6. B. The angle at the centre is twice the angle at the circumference

  7. 7. 34

  8. 8. 55

  9. 9. 102

  10. 10. 18

  11. 11. 105

  12. 12. C. Tangents from an outside point are equal in length

  13. 13. 59

  14. 14. 65

  15. 15. 17

  16. 16. 36

HSG.C.A.3 Worksheet: Circle theorems | Eurekami