Q: 5 Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, and Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is each, what is the distance between Reshma and Mandip?
Given: From figure, R, S and, M are the positions of Reshma, Salma, Mandip respectively.
So, RS = SM = 6 cm
Construction: Join OR, OS, RS, RM and OM. Draw .
Proof:
In ORS,
OS = OR and (by construction )
So, RL = LS = 3cm (RS = 6 cm )
In OLS, by Pythagoras theorem,
In ORK and OMK,
OR = OM (Radii)
ROK = MOK (Equal chords subtend equal angle at centre)
OK = OK (Common)
ORK OMK (By SAS)
RK = MK (CPCT)
Thus,
area of ORS =...............................1
area of ORS =.............................2
From 1 and 2, we get
Thus,