Three girls Reshma,Salma,and Mandip are playi | vedclass

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

Question

(B) Let the positions of Reshma,Salma,and Mandip be $R, S,$ and $M$ respectively on the circle with center $O$ and radius $5 \, m$.Given $RS = SM = 6

Vedclass · Accepted Answer

$9.6$

Vedclass · Answer

(B) Let the positions of Reshma,Salma,and Mandip be $R, S,$ and $M$ respectively on the circle with center $O$ and radius $5 \, m$.Given $RS = SM = 6 \, m$.Since equal chords subtend equal angles at the center,$\angle ROS = \angle SOM$.Let $OP$ be the perpendicular from $O$ to $RM$,intersecting $RM$ at $P$ and $OS$ at $K$.Since $RS = SM$,$OS$ is the perpendicular bisector of $RM$. Thus,$RM \perp OS$ and $RP = PM$.Let $OK = x$. Then $KS = 5 - x$.In $\Delta ORK$,$RK^2 = OR^2 - OK^2 = 5^2 - x^2 = 25 - x^2$.In $\Delta RSK$,$RK^2 = RS^2 - KS^2 = 6^2 - (5 - x)^2 = 36 - (25 - 10x + x^2) = 11 + 10x - x^2$.Equating the two expressions for $RK^2$: $25 - x^2 = 11 + 10x - x^2$.$10x = 14 \Rightarrow x = 1.4 \, m$.Now,$RK^2 = 25 - (1.4)^2 = 25 - 1.96 = 23.04$.$RK = \sqrt{23.04} = 4.8 \, m$.Since $RM = 2 	imes RK$,$RM = 2 	imes 4.8 = 9.6 \, m$.

Similar Questions

If the non-parallel sides of a trapezium are equal,prove that it is cyclic.

Prove that a cyclic parallelogram is a rectangle.

Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.

If two equal chords of a circle intersect within the circle,prove that the segments of one chord are equal to corresponding segments of the other chord.

Two circles of radii $5\, cm$ and $3\, cm$ intersect at two points and the distance between their centres is $4\, cm.$ Find the length of the common chord. (in $, cm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module