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Question
O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8, 6) and (10, 0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.
Solution
Note: Since OD is perpendicular to AB, OD bisect the chord
D is the mid-point of AB
Mid−point of a line = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
Mid−point of AB(D) = `((8 + 10)/2, (6 + 0)/2)`
= `(18/2, 6/2)`
= (9, 3)
Mid−point of OD = `((0 + 9)/2, (0 + 3)/2)`
= `(9/2, 3/2)`
Mid−point of OD is `(9/2, 3/2)`
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