CAIE P1 2021 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicCircles

10 Points \(A ( - 2,3 ) , B ( 3,0 )\) and \(C ( 6,5 )\) lie on the circumference of a circle with centre \(D\).
  1. Show that angle \(A B C = 90 ^ { \circ }\).
  2. Hence state the coordinates of \(D\).
  3. Find an equation of the circle.
    The point \(E\) lies on the circumference of the circle such that \(B E\) is a diameter.
  4. Find an equation of the tangent to the circle at \(E\).