If ABC is a quarter circle and a circle is inscribed in it and if AB = 1 cm, find radius of smaller circle.

Foundation

Mathematics Foundation

distance formulae

Properties of Circle

Rationalisation

Question

If ABC is a quarter circle and a circle is inscribed in it and if AB = 1 cm, find radius of smaller circle.

$\sqrt{2} - 1$

$1 - 2 \sqrt{2}$

$\sqrt{2} - 1 / 2$

$(\sqrt{2} - 1) / 2$

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In right tangle triangle OAB
AB² + BO² = OA²
x² + x² = (1 – x)²
2x² = x² + 1 – 2x
x² + 2x – 1 = 0
$x = \frac{- 2 \pm \sqrt{4 + 4}}{2}$
$x = - 1 \pm \sqrt{2}$
taking positive sign
$x = \sqrt{2} - 1$