search
Log In
Welcome to GO Mechanical, where you can ask questions and receive answers from other members of the community.
1 vote

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is ___________

  1. $\frac{1}{8}$
  1. $\frac{1}{6}$
  1. $\frac{1}{4}$
  1. $\frac{1}{2}$
in Numerical Ability 4.9k points
recategorized by

1 Answer

0 votes

 

Given that, the  $\triangle ABC$ is an equilateral triangle.

Let the radius of the inscribed circle be $r\;\text{cm},$ and radius of the circumscribed circle be $R\;\text{cm}.$

In $\triangle OBD,\angle OBD = 30^{\circ},\angle ODB = 90^{\circ}$

$\implies \sin 30^{\circ} = \dfrac{r}{R} $

$\implies\dfrac{1}{2}= \dfrac{r}{R}$

$\implies R = 2R$

Let the area of the inscribed circle be $A_{I}\;\text{cm}^{2}$ and the area of the circumscribed circle  be $A_{C}\;\text{cm}^{2}.$

$\implies \dfrac{A_{I}}{A_{C}} = \dfrac{\pi r^{2}}{\pi R^{2}} = \dfrac{r^{2}}{(2r)^{2}} = \dfrac{1}{4}.$

So, the correct answer is $(C).$

5.7k points 3 6 14
Answer:

Related questions

1 vote
1 answer
In the above figure, $\textsf{O}$ is the center of the circle and, $\textsf{M}$ and $\textsf{N}$ lie on the circle. The area of the right triangle $\textsf{MON}$ is $50\;\text{cm}^{2}$. What is the area of the circle in $\text{cm}^{2}?$ $2\pi$ $50\pi$ $75\pi$ $100\pi$
asked Feb 22 in Numerical Ability gatecse 1.6k points
0 votes
0 answers
Let $S_{1}$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x - 1 \mid \leq 2$ and $ \mid y+2 \mid \leq 3$. Let $S_{2}$ be the plane figure given by the inequalities $x-y \geq -2, y \geq 1$, and $x \leq 3$. Let $S$ be the union of $S_{1}$ and $S_{2}$. The area of $S$ is. $26$ $28$ $32$ $34$
asked Feb 27, 2017 in Numerical Ability Arjun 24.6k points
1 vote
1 answer
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _________ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{1}{32}$
asked Mar 1 in Spatial Aptitude jothee 4.9k points
1 vote
1 answer
Five persons $\text{P, Q, R, S}$ and $\text{T}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{T}$ cannot be seated at either end of the row. $\text{P}$ should not be seated adjacent ... is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is: $2$ $3$ $4$ $5$
asked Mar 1 in Numerical Ability jothee 4.9k points
1 vote
1 answer
A digital watch $\text{X}$ beeps every $30$ seconds while watch $\text{Y}$ beeps every $32$ seconds. They beeped together at $\text{10 AM}$. The immediate next time that they will beep together is ____ $\text{10.08 AM}$ $\text{10.42 AM}$ $\text{11.00 AM}$ $\text{10.00 PM}$
asked Mar 1 in Numerical Ability jothee 4.9k points
...