Let ABCD and AEFG be squares of sides 4 and 2 units respectively. the point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies :

Question

Let ABCD and AEFG be squares of sides 4 and 2 units respectively. the point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies : [2024]

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(2)

Let r be the radius of circle and centre at C(r, r).

Then, $F C^{2} = r^{2}$

$\Rightarrow {(r - 2)}^{2} + {(r - 2)}^{2} = r^{2}$

$\Rightarrow r^{2} - 8 r + 8 = 0$ .

Solution

Q.
Let ABCD and AEFG be squares of sides 4 and 2 units respectively. the point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies : [2024]

1 $2 r^{2} - 4 r + 1 = 0$

2 $r^{2} - 8 r + 8 = 0$

3 r = 1

4 $2 r^{2} - 8 r + 7 = 0$

Ans.
(2)

Let r be the radius of circle and centre at C(r, r).

Then, $F C^{2} = r^{2}$

$\Rightarrow {(r - 2)}^{2} + {(r - 2)}^{2} = r^{2}$

$\Rightarrow r^{2} - 8 r + 8 = 0$ .

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Solution

Q. Let ABCD and AEFG be squares of sides 4 and 2 units respectively. the point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies : [2024]

1 2r2–4r+1=0

2 r2–8r+8=0