If in two circles,arcs of the same length sub | vedclass

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

Question

(B) Let the radii of the two circles be $r_{1}$ and $r_{2}$.Let an arc of length $l$ subtend an angle of $60^{\circ}$ at the centre of the circle of r

Vedclass · Accepted Answer

$5: 4$

Vedclass · Answer

(B) Let the radii of the two circles be $r_{1}$ and $r_{2}$.Let an arc of length $l$ subtend an angle of $60^{\circ}$ at the centre of the circle of radius $r_{1}$,and an arc of the same length $l$ subtend an angle of $75^{\circ}$ at the centre of the circle of radius $r_{2}$.We know that $l = r 	heta$,where $	heta$ is in radians.Convert the angles to radians:$60^{\circ} = 60 	imes \frac{\pi}{180} = \frac{\pi}{3} 	ext{ radians}$.$75^{\circ} = 75 	imes \frac{\pi}{180} = \frac{5\pi}{12} 	ext{ radians}$.Since the arc lengths are equal,$l = r_{1} 	imes \frac{\pi}{3} = r_{2} 	imes \frac{5\pi}{12}$.Dividing both sides by $\pi$,we get $\frac{r_{1}}{3} = \frac{5r_{2}}{12}$.Therefore,$\frac{r_{1}}{r_{2}} = \frac{5 	imes 3}{12} = \frac{15}{12} = \frac{5}{4}$.The ratio of their radii is $5: 4$.

If in two circles,arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre,find the ratio of their radii.

Similar Questions

From three non-collinear points,we can draw:

If the length of the chord $2x + 3y + k = 0$ of the circle $x^2 + y^2 - 2x + 4y - 11 = 0$ is $2\sqrt{3}$,then the sum of all possible values of $k$ is

The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is

If one end of a diameter of the circle $x^2 + y^2 + 2x + 4y - 3 = 0$ is $(1, 0)$,then the other end of the diameter is:

The circle $4x^2+4y^2-12x-12y+9=0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module