Question

Let $ABCD$ be a square of side length $1$. and $\Gamma$ a circle passing through $B$ and $C$, and touching $AD$. The radius of $\Gamma$ is

• A. $\frac{3}{8}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{5}{8}$

Answer 1

The correct option is D $\frac{5}{8}$

$PC=r$
${PC}^2=r^2$
${(r-1)}^2+{(\frac{1}{2}-1)}^2=r^2$
$1-2r+\frac{1}{4}=0$
$r=\frac{5}{8}$