Q. 54.0( 396 Votes )

Three girls Reshm

Answer :

To Find: Distance between Reshma and Mandip
Given: Distance between Reshma and Salma and between Salma and Mandip is 6m
Diagram:

Explanation:

Draw perpendicular OA on RS.

As OA ⊥ RS,

RA = AS

Let R, S and M be the positions of Reshma, Salma and Mandip.

 Now in ΔOAR by Pythagoras theorem,

OR2 = OA2 + RA2

OA2 = 52 - 32

OA2 = 25 – 9

OA2 = 16

OA = 4

Now we know,

Area of triangle = ½ × B × H

Area ΔORS = ½ × OS × RK

               = ½ × 5 × RK  ….. (1)

Also,

Area ΔORS = ½ × OA × RS

               = ½ × 4 × 6
               = 12    ….. (2)

From (1) and (2),

½ × 5 × RK = 12


RK = 4.8 m
As the perpendicular from the centre of a circle bisects the chord.

As RM = 2RK

          = 2× 4.8

          = 9.6 m

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