$∠ A C B = 90^{o}$ Radius of bigger circle = 2 cm Find the radius of scroller circle.

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Solution

We know that,
$(2 + x)^{2} = (2 - x)^{2} + (2 - x)^{2}$
$x^{2} + 4 x + 4 = 2 x^{2} - 4 x + 8$
$x^{2} - 8 x + 4 = 0$
$x = 4 \pm 2 \sqrt{3}$

Since, $x < 2$

$∴ x = 4 - 2 \sqrt{3}$

Hence, this is the answer.

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∠ACB=90o Radius of bigger circle = 2 cm Find the radius of scroller circle.

We know that,(2+x)2=(2−x)2+(2−x)2x2+4x+4=2x2−4x+8x2−8x+4=0x=4±2√3Since, x<2∴x=4−2√3Hence, this is the answer.

$∠ A C B = 90^{o}$ Radius of bigger circle = 2 cm Find the radius of scroller circle.

We know that,
$(2 + x)^{2} = (2 - x)^{2} + (2 - x)^{2}$
$x^{2} + 4 x + 4 = 2 x^{2} - 4 x + 8$
$x^{2} - 8 x + 4 = 0$
$x = 4 \pm 2 \sqrt{3}$

Since, $x < 2$

$∴ x = 4 - 2 \sqrt{3}$

Hence, this is the answer.