Question

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

• A. $\sqrt{2}-1$
• B. $\frac{\sqrt{2}-1}{2}$
• C. $\frac{\sqrt{2}+1}{2}$
• D. $1-2\sqrt{2}$

Answer 1

The correct option is A $\sqrt{2}-1$

$OE=OD=OF$ (Radius of inner circle)

$(B{)}^2=(BD{)}^2+(OD{)}^2$

$(OB{)}^2=r^2+r^2$

$OB=\sqrt{2}r$

$BF=1cm$

$OB+OF=1$

$\sqrt{2}r+r=1$

$r=\frac{1}{\sqrt{2}+1}$

$r=(\sqrt{2}-1)cm$