GEOMETRY AND APPLICATIONS 111 - CIRCLE GEOMETRY REVIEW

1. A chord is 8 cm from the centre of a circle. The radius of the circle is 13 cm. Determine the length of the chord.

2. A 10 cm chord is 4 cm from the centre of a circle. Find the radius of the circle.

3. A security camera turns back and forth through an angle of 170o. The image from the camera is clear to a maximum distance of 15 m. What is the area of sector that the camera can clearly survey?

4. A triangle has vertices R(17, 16), S(1, 4), and T(7, − 4). a. Is this a right triangle? b. Find the midpoints of RT and RS. c. Determine whether or not the line joining these midpoints is parallel to ST.

5. A circle has centre (3, − 1) and radius 10 units. Determine if the point ( − 4, − 8) is inside, on, or outside the circle.

6. What is the distance from point (8, 15) to the origin?

7. Points D, E, F, G lie in order on a circle. DF is a diameter and DE = DG. Prove FE = FG.

8. If two tangents from an external point P meet a circle at A and B, prove that

9. Points A, B, C are on a circle. If the tangent at A is parallel to the chord BC, prove that ΔABC is isosceles.

10. A triangle has vertices F(0, 4), H(6, 0), and S(2, − 4). a. Calculate the length of the median from S. b. Find the slope of the median from S. c. Find the slope of the altitude from H.

11. Determine the centre and radius and sketch the circle x2 + y2 − 4x + 12y + 4 = 0. Write the mapping rule that expresses this circle as a transformation of the unit circle.

12. A circle has centre (− 2, 5) and radius 3. a. Write the equation of this circle in transformational form. b. Write the equation of this circle in general form. c. If this circle is moved 3 units to the left and 2 units up, what are the coordinates of the new centre?

13. The circle with equation (x − 3)2 + (y + 7)2 = 81 has its radius enlarged by a factor of 2. What is the equation of the new circle?

14. The equation of a circle is given by x2 + y2 + mx − 5y + 10 = 0. If point P( − 1, 4) lies on the circle, find the value of m.

15. State the centre and the length of the minor axis and sketch the ellipse 轾12 轾 1 2 (x- 2) + ( y + 6) = 1 臌犏4 臌犏 8

16. State the measures of the letters indicated in each diagram. Please note that the centre of each circle is marked and that the diagrams are not drawn to scale.