CAIE P1 2020 November — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionNovember
TopicCircles

11 A circle with centre \(C\) has equation \(( x - 8 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 100\).
  1. Show that the point \(T ( - 6,6 )\) is outside the circle.
    Two tangents from \(T\) to the circle are drawn.
  2. Show that the angle between one of the tangents and \(C T\) is exactly \(45 ^ { \circ }\).
    The two tangents touch the circle at \(A\) and \(B\).
  3. Find the equation of the line \(A B\), giving your answer in the form \(y = m x + c\).
  4. Find the \(x\)-coordinates of \(A\) and \(B\).
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.