Let A_0 A_1 A_2 A_3 A_4 A_5 be a regular hexa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) In a regular hexagon inscribed in a circle of radius $R = 1$,the side length is equal to the radius,so $A_0A_1 = A_1A_2 = 1$.The segment $A_0A_4$

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(C) In a regular hexagon inscribed in a circle of radius $R = 1$,the side length is equal to the radius,so $A_0A_1 = A_1A_2 = 1$.The segment $A_0A_4$ is a chord of the circle. In a regular hexagon,the angle subtended by a side at the center is $60^\circ$. The segment $A_0A_4$ subtends an angle of $120^\circ$ at the center (or $240^\circ$ depending on the arc).Alternatively,using the geometry of the hexagon,$A_0A_4$ is the distance between two vertices separated by one vertex $(A_5)$. In a circle of radius $R$,the length of a chord subtending an angle $	heta$ at the center is $2R \sin(	heta/2)$.For $A_0A_4$,the angle subtended at the center is $120^\circ$,so $A_0A_4 = 2(1) \sin(120^\circ/2) = 2 \sin(60^\circ) = 2 	imes \frac{\sqrt{3}}{2} = \sqrt{3}$.The product of the lengths $A_0A_1$,$A_1A_2$,and $A_0A_4$ is $(1) 	imes (1) 	imes (\sqrt{3}) = \sqrt{3}$.

Let $A_0 A_1 A_2 A_3 A_4 A_5$ be a regular hexagon inscribed in a circle of unit radius. The product of the lengths of the line segments $A_0A_1$,$A_1A_2$,and $A_0A_4$ is

Similar Questions

The number of common tangents to the circles $x^2+y^2-x=0$ and $x^2+y^2+x=0$ is/are:

If $(6, -k)$ and $(-3, 2)$ are conjugate points with respect to the circle $x^2 + y^2 + 6x + 4y + 12 = 0$,then $k$ equals:

The angle subtended at the centre of a circle of radius $3 \text{ metres}$ by an arc of length $1 \text{ metre}$ is equal to

If $x^2 + y^2 + 2gx + 2fy + c = 0$ is the equation of the smallest circle passing through $(1, 2)$ and touching the line $x + y - 7 = 0$,then the value of $(g + 2f + 3c)$ is -

Does the point $(-2.5, 3.5)$ lie inside,outside,or on the circle $x^{2}+y^{2}=25$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module