The centre C of the given circlee = (2, 2) P(5, 4) is a point on the circle. Join P to C and extend it to meet the circle at the other extremity Q of the diameter. Now PQ is a diameter of the circle with C as its midpoint. The the coordinates of Q be (x, y) The coordinates of midpoint are (2, 2) = [ (x +5)/2, (y + 4)/2] =%3E (x + 5)/2 = 2; =%3E x = 4 — 5 = —1 =%3E (y + 4) = 2; =%3E y = 4 — 4 = 0 The extremities of the diameter are (—1, 0) and (5, 4). Diameter² = [5 —(—1)]² + [ 4 —0]² = 6² + 4² = 36 + 16 = 52 Diameter = 2√13 We could have easily found the radius from the centre and the given point on the circumference. The radius r² = (5 — 2)² + (4 — 2)² = 9 +4 = 13 Radius r = √13 And diameter = 2 r = 2 √13
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-lukelaws