Question

5. Three girls Reshma, Salma and Mandip are
playing a game by standing on a circle of radius
5m drawn in a park. Reshma throws a ball to
Salma, Salma to Mandip. Mandip to Reshma. If
the distance between Reshma and Salma and
between Salma and Mandip is om each, what is
the distance between Reshma and Mandip?
answer step wise step​

Answer 1

In ∆ ROS and ∆MOS,

OR = OM (radii)

RS= MS(given)

OS= OS (common)

therefore, By SSS congruence rule,

∆ROS is congruent to ∆MOS

Angle RSP = Angle MSP (by CPCT)

In ∆RSP and ∆MSP,

RS=MS(given)

SP=SP(common)

angleRSP = angleMSP (proved above)

therefore, ∆RSP is congruent to ∆MSP (by SAS congruence rule)

by CPCT = angleRPS=angleMPS

and RP=MP

Now,

angleRPS + angleMPS= 180°

angleRPS = 90°

Now, In ∆RPS

RS^2 = RP^2 + PS^2

6^2 = RP^2 + x^2

Therefore, RP^2 = 6^2 - x^2 ........ (1)

In ∆RPO, angleP = 90°

RO^2= RP^2 + OP^2

5^2 = RP^2 -(5-x) ^2

RP^2 = 25 -(5-x) ^2....... (2)

From (1) &(2)

36-x^2 = 25-(25-10x+x^2)

36-x^2 = 25-25 +10x +x^2.

10x= 36

x= 3.6cm

Therefore, RP= 36-12.96

= 23.04

RP= 4.8m

2RP = RM.

therefore, RM = 2×4.8

RM= 9.6cm