Download App

STD 11 - 10.1 circle and system of circle — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.1 circle and system of circle4 Marks
MCQ
Let $A B C D$ be a quadrilateral with area $18$ , with side $A B$ parallel to the side $C D$ and $A B=2 C D$. Let $A D$ be perpendicular to $A B$ and $C D$. If a circle is drawn inside the quadrilateral $A B C D$ touching all the sides, then its radius is
  • A
    $3$
  • ✓
    $2$
  • C
    $3 / 2$
  • D
     $1$
✓

Answer

Correct option: B.
$2$
b
$18=\frac{1}{2}(3 \alpha)(2 \mathrm{r}) \Rightarrow \alpha \mathrm{r}=6$

Line $y=-\frac{2 r}{\alpha}(x-2 \alpha)$ is tangent to $(x-r)^2+$ $(y-r)^2=r^2$

$2 \alpha=3 \mathrm{r}$ and $\alpha \mathrm{r}=6$

$\mathrm{r}=2 \text {. }$

Alternate

$ \frac{1}{2}(x+2 x) \times 2 r=18 $

$ x r=6 $

$ \tan \theta=\frac{x-r}{r} \quad \tan (90-\theta)=\frac{2 x-r}{r} $

$ \frac{x-r}{r}=\frac{r}{2 x-r} $

$ x(2 x-3 r)=0 $

$ x=\frac{3 r}{2}$

From $(1)$ and $(2)$

$r=2 \text {. }$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The sum of the first $20$ terms common between the series $3 +7 + 1 1 + 15+ ... ......$ and $1 +6+ 11 + 16+ ......$, is
→
For a natural number $n$, let $a _{ n }=19^{ n }-12^{ n }$. Then, the value of $\frac{31 \alpha_{9}-\alpha_{10}}{57 \alpha_{8}}$ is
→
The normal to the parabola ${y^2} = 8x$ at the point $(2, 4)$ meets the parabola again at the point
→
A value of $\theta  \in  (0, \pi /3)$, for which $\left| {\begin{array}{*{20}{c}}
  {1 + {{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\ 
  {{{\cos }^2}\,\theta }&{1 + {{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\ 
  {{{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{1 + 4\,\cos \,6\theta } 
\end{array}} \right| = 0$, is
→
In a single throw of two dice, the probability of getting more than $7$ is
→
If mean and standard deviation of $5$ observations $x_1 ,x_2 ,x_3 ,x_4 ,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1 ,x_2 ,.....,x_3$ and $-50$ is equal to
→
Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0.$ If the equation to one diagonal is $11x + 7y = 9,$ then the equation of the other diagonal is
→
The distance between the directrices of the hyperbola $x = 8\sec \theta ,\;\;y = 8\tan \theta $ is
→
How many numbers, lying between $99$ and $1000$ be made from the digits $2, 3, 7, 0, 8, 6$ when the digits occur only once in each number
→
A board has 16 squares as shown in the figure :
Image
out of these 16 squares, two squares are chosen at random. the probality that they have no side in common is :
→