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The radius of the circle whose endpoints of diameter are (24,1) and $(2, 23)$ The radius of the circle whose endpoints of diameter are (24,1) and is ____units.

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Detailed Solution

The radius of the circle whose endpoints of diameter are (24,1) and (2, 23) is

112

units.
We have been given,
The radius of the circle whose endpoints of diameter are (24,1) and

(2, 23)

.
Using the distance formula,

D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

The radius of the circle

r = \frac{d}{2} (d = diameter)

.
So, the length of the diameter is,
Substituting

x_{2} = 2, x_{1} = 24, y_{2} = 23, and y_{1} = 1

, in the formula,

d = \sqrt{{(2 - 24)}^{2} + {(23 - 1)}^{2}}

\Rightarrow \sqrt{(484 + 484)}

\Rightarrow 22 \sqrt{2} units

Radius of the circle ‘r’,

r = \frac{d}{2}

\Rightarrow \frac{22 \sqrt{2}}{2}

\Rightarrow 11 \sqrt{2} units

Therefore, the radius of the circle is

112

units.

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