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

Answer 1

hope this answer will help you
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Answer 2

Answer:

(9/2, 3/2)

Step-by-step explanation:

Hi,

Given O(0, 0) is the center of the circle

AB is the chord of the circle whose points A and B are given by

A(8,6) and B(10, 0)

Given that OD is the perpendicular drawn from the center to the chord.

But, we know that perpendicular drawn to any chord of the circle,

will bisect the chord,

Hence, Since OD is perpendicular to AB, D will bisect the chord AB.

So, D is the midpoint of AB.

Hence, the co-ordinates of D using mid-point formula will be

D(8 + 10/2, 6 + 0/2)

D(9, 3).

So, Now Having O (0, 0) and D(9, 3), Midpoint of OD will be

(9 + 0/2, 3 + 0/2)

= (9/2, 3/2)

Hope, it helps !