A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertex, the radius of the circle can be

Question

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertex, the radius of the circle can be (A) 2-√2 (B) √2-1 (C) 2+√3 (D) (1/√2)

Tardigrade Admin · Accepted Answer

l. (r-1)2+(r-1)2=r2 ⇒ r2-4 r+2=0 ⇒ r=(4+√16-8/2)=(4 ± 2 √2/2)=2 ± √2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d27df61933bd403daee182666ee8ab81-.png" />

Q. $A BC D$ is a square of unit area. A circle is tangent to two sides of $A BC D$ and passes through exactly one of its vertex, the radius of the circle can be

$2 - 2$

$2 - 1$

$2 + 3$

$\frac{1}{2}$

l. $(r - 1)^{2} + (r - 1)^{2} = r^{2}$
$\Rightarrow r^{2} - 4 r + 2 = 0$
$\Rightarrow r = \frac{4 + 16 - 8}{2} = \frac{4 \pm 2 2}{2} = 2 \pm 2$

Q. ABCD is a square of unit area. A circle is tangent to two sides of ABCD and passes through exactly one of its vertex, the radius of the circle can be

2−2​

2​−1

2+3​

2​1​