Circle Geometry Review Sheet - Fredericton High School

Math 112AExam Review Sheet – Circle Geometry1. Write the converse of each of the following. If the statement and converse are bothtrue, then rewrite the statement using “iff’. If the converse is not true, explain why.a. If two chords are equidistant from the centre of a circle, then they are equal inlength.b. If two triangles are congruent, then their corresponding angles are equal.2. A 10 cm chord is 4 cm from the centre of a circle. Find the radius of the circle.3. A triangle has vertices R(l7,16), 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.4. Points D, E, F, & G lie in order on a circle. DF is a diameter and DE = DG. Prove thatFE = FG.5. If two tangents from an external point P meet a circle at A and B, prove that∠ PAB = ∠ PBA .6. Points A, B and C are on a circle. If the tangent at A is parallel to the chord BC, provethat triangle ABC is isosceles.7. 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.2 28. Determine the centre and radius of the circle x + y − 4x + 12y+ 4 = 0 .Write the mapping rule that expresses this circle as a transformation of the unitcircle. Sketch the circle.9. 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.10. The equation of a circle is given by If point V(-1,4) lies on the circle,find the value of m.11. Determine the lengths of the major and minor axes, and sketch the ellipse.12. A pizza with a diameter of 30 cm is cut into 12 equal pieces. Find the area of oneslice.13. Find the missing sides and angles.

14. Determine the equation of the following in transformational form.a. b.