- Home
- Standard 11
- Mathematics
10-1.Circle and System of Circles
normal
In the figure, $A B C D$ is a unit square. A circle is drawn with centre $O$ on the extended line $C D$ and passing through $A$. If the diagonal $A C$ is tangent to the circle, then the area of the shaded region is
A
$\frac{9-\pi}{6}$
B
$\frac{8-\pi}{6}$
C
$\frac{7-\pi}{4}$
D
$\frac{6-\pi}{4}$
(KVPY-2017)
Solution
(d)
Given, $A B C D$ is a square
$A B=C D=A D=B C=1$
$A C$ is tangent of circle
$\angle O A C =90^{\circ}$
$\angle C A D =45^{\circ}$
$\angle O A D =45^{\circ}$
$O A =\sqrt{2}$
$\therefore$ Area of shaded region
$=$ Area of square $+$ Area of
$\triangle A O D-$ Area of sector
$=1+\frac{1}{2} \times 1-\frac{45}{360} \times(\sqrt{2})^2 \cdot \pi$
$=1+\frac{1}{2}-\frac{\pi}{4}-\frac{3}{2}-\frac{\pi}{4}-\frac{6-\pi}{4}$
Standard 11
Mathematics
