Question

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 6 m each, what is the distance between Reshma and Mandip?

Answer 1

Data: Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 cm drawn in a park. Distance between Reshma and Salma and between Salma and Mandip is 6 cm. each. 

To Prove: Distance between Reshma and Mandip = ? RM = ?

Construction: Draw OX⊥RS and OY⊥SM. OR, OS and OM are joined. 

Proof: OR = OS = OM = 5 m. 

RX = XS = 3 m. 

Now, in ⊥∆ORX, 

OR² = OX² + RX² 

(5)² = (OX)² + (3)² 

25 = OX² + 9 

25 – 9 = OX² 

16 = OX² 

OX² = 16 

∴ OX = 4 WI …………… (i) 

In quadrilateral ORSM, OR = OM and SR = SM 

∴ ORSM is a kite. 

Diagonals of a kite bisect at right angle. 

∠RAS = 90° 

∴ RA = AM.

Now, RM = 2RC = 2 × 4.8 = 9.8 m 

∴ RM = 9.8 m. 

∴ Distance between Reshma and Mandip is 9.8 m.