<p> GEOMETRY AND APPLICATIONS 111 - CIRCLE GEOMETRY REVIEW</p><p>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.</p><p>2. A 10 cm chord is 4 cm from the centre of a circle. Find the radius of the circle.</p><p>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?</p><p>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.</p><p>5. A circle has centre (3, − 1) and radius 10 units. Determine if the point ( − 4, − 8) is inside, on, or outside the circle.</p><p>6. What is the distance from point (8, 15) to the origin?</p><p>7. Points D, E, F, G lie in order on a circle. DF is a diameter and DE = DG. Prove FE = FG.</p><p>8. If two tangents from an external point P meet a circle at A and B, prove that <PAB = <PBA</p><p>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.</p><p>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.</p><p>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. </p><p>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?</p><p>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?</p><p>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.</p><p>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</p><p>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. </p>