Download 4.6 – Geometry – Circle Properties (Answers)

4.6 – Geometry – Circle Properties (Answers)
1. (a) (i) 114 (b) 74
2. (a) (i) 41o (ii) Angles in same segment (are equal) (b) (i) 75o (ii) Angle at centre/middle is
not 2 x angle at circumference / edge / perimeter / arc
or Angle PQT ≠ QPT or PRS ≠ RSQ oe or ≠
3. 3.63
4. Accept
x + y = 69 or
− / =
/
(where <OCD
= ∠<ODC = y)
23
5. 4.46 or 4.45
6. (a) 32 (b) (i) 122 (ii) (ii) Opposite angles in a cyclic quad ( =180°)
7. (a) 7.27 (b) 4
8. 28
9. 64
10. 4.5 oe
11. (a)(i) 6 (ii) Tangents from a point to a circle are equal in length (b) 67.4
12. 122
13. (a) 67 (b)(i) 113
14. 32
15. 52.1
16. (a) (i) 112 (ii) (a) (ii) Opposite angles of a cyclic quadrilateral (add up to 180) (b) (i) 136 (ii) (b) (ii)
Angle at the centre/ middle is twice / (2 times)/ double angle at circumference/ edge/ perimeter
(c ) 68
17. 6
18. (a) 54 (b) 34
19. (a) 54 Angle between tangent and radius
is 900 (b) 83
20. 3 ½ oe
21. 4.875
22. (a) Angle between tangent and radius is 900 (b) 22
23. 10.3
24. (a) 20 (b) 60