If the centre of a circle is (2a,a-7) ,then Find the value of a , if the circle passes through the point (11,-9) and has diameter `10sqrt(2)` units .

Explanation

To solve the problem step by step, we will follow the given information about the circle and apply the distance formula to find the value of \( a \).

### Step 1: Understand the given information
The center of the circle is given as \( (2a, a - 7) \). The diameter of the circle is given as \( 10\sqrt{2} \), which means the radius \( r \) is half of the diameter:
\[ r = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \]

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