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Maths-

General

Easy

Question

The area of the circle and the area of a regular polygon of n sides, and of perimeter equal to that of the circle are in the ratio of

tan $(\frac{π}{3})$ : $\frac{π}{n}$
cot $(\frac{π}{n})$ : $\frac{π}{n}$
sin $(\frac{π}{n})$ : $\frac{π}{n}$
cos $(\frac{π}{n})$ : $\frac{π}{n}$

The correct answer is: tan $open parentheses fraction numerator pi over denominator 3 end fraction close parentheses$ : $fraction numerator pi over denominator n end fraction$

The perimeter of a regular polygon of n sides = 2nr sin $fraction numerator pi over denominator n end fraction$
If the radius of the circle is a then 2a = 2nr sin $fraction numerator pi over denominator n end fraction$ ... (i)
Now area of polygon = n $open parentheses fraction numerator 1 over denominator 2 end fraction cross times 2 r sin invisible function application fraction numerator pi over denominator n end fraction r cos invisible function application fraction numerator pi over denominator n end fraction close parentheses$
ratio of areas of circle and polygon
= $fraction numerator pi a to the power of 2 end exponent over denominator n r sin invisible function application fraction numerator pi over denominator n end fraction cos invisible function application fraction numerator pi over denominator n end fraction end fraction$ = $open parentheses tan invisible function application fraction numerator pi over denominator n end fraction close parentheses$ : $fraction numerator pi over denominator n end fraction$ (from (i))

Related Questions to study

If a right-angled ABC of maximum area is inscribed within a circle of radius R, then-

If a right-angled ABC of maximum area is inscribed within a circle of radius R, then-

The motion of a particle along a straight line is described by equation :
$x equals 8 plus 12 t minus t to the power of 3 end exponent$
Where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is

The motion of a particle along a straight line is described by equation :
$x equals 8 plus 12 t minus t to the power of 3 end exponent$
Where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is

Physics-General

A ball is thrown vertically upwards with a velocity of $25 blank m s to the power of negative 1 end exponent$ from the top of a tower of height 30 m. How long will it travel before it hits ground?

A ball is thrown vertically upwards with a velocity of $25 blank m s to the power of negative 1 end exponent$ from the top of a tower of height 30 m. How long will it travel before it hits ground?

Physics-General

parallel

In a triangle ABC, let ÐC = $fraction numerator pi over denominator 2 end fraction$ . If r is the in radius and R is the circumradius of the triangle, then 2(r + R) is equal to -

In a triangle ABC, let ÐC = $fraction numerator pi over denominator 2 end fraction$ . If r is the in radius and R is the circumradius of the triangle, then 2(r + R) is equal to -

Let A0 A1 A2 A3 A4 A5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A0A1, A0A2 , and A0A4 is -

Let A0 A1 A2 A3 A4 A5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A0A1, A0A2 , and A0A4 is -

Let L sin q = 10 + log sin q. The number of triangles ABC such that log b + 10 = log c + L sin B is-

Let L sin q = 10 + log sin q. The number of triangles ABC such that log b + 10 = log c + L sin B is-

parallel

If for a DABC, cot A. cot B. cot C > 0 then the triangle is-

If for a DABC, cot A. cot B. cot C > 0 then the triangle is-

In a triangle PQR as shown in figure given that x : y : z :: 2 : 3 : 6, then the value of ÐQPR is -

In a triangle PQR as shown in figure given that x : y : z :: 2 : 3 : 6, then the value of ÐQPR is -
Maths-General

The in-radius of the triangle formed by the axes and the line 4x + 3y – 12 = 0 is -

The in-radius of the triangle formed by the axes and the line 4x + 3y – 12 = 0 is -

parallel

In a  ABC if r1 = 2r2 = 3r3, then -

In a  ABC if r1 = 2r2 = 3r3, then -

The area of a circle is A1 and the area of a regular pentagon inscribed in the circle is A2. Then A1 : A2 is -

The area of a circle is A1 and the area of a regular pentagon inscribed in the circle is A2. Then A1 : A2 is -

If A, A1, A2, A3 be the area of the in-circle and ex-circles, then $fraction numerator 1 over denominator square root of A subscript 1 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 2 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 3 end subscript end root end fraction$ is equal to-

If A, A1, A2, A3 be the area of the in-circle and ex-circles, then $fraction numerator 1 over denominator square root of A subscript 1 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 2 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 3 end subscript end root end fraction$ is equal to-

parallel

If $fraction numerator r over denominator r subscript 1 end subscript end fraction$ = $fraction numerator r subscript 2 end subscript over denominator r subscript 3 end subscript end fraction$ , then -

If $fraction numerator r over denominator r subscript 1 end subscript end fraction$ = $fraction numerator r subscript 2 end subscript over denominator r subscript 3 end subscript end fraction$ , then -

16R2 r r1 r2 r3 =

16R2 r r1 r2 r3 =

If a , b, c are in A.P., then r1, r2, r3 are in

If a , b, c are in A.P., then r1, r2, r3 are in

parallel

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