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Ex 10.4, 5 - Three girls Reshma, Salma and Mandip are - Equal chords and their distance from centre

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  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Ex 10.4, 5 Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m 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? Given: Let Reshma , Salma and Mandip be donated by points R,S & M resp. Given radius = 5 m & RS = 6m, SM =6m To find: Length of RM Construction: Join OR, OS, OM Let RM intersect OS at X Solution: In Δ ORS & Δ OMS OR = OM OS = OS RS = SM Δ ORS ≅ Δ OMS ∴ ∠ ROS = ∠ MOS In Δ ORX & Δ OMX OR = OM ∠ ROX = ∠ MOX OX = OX Δ ORX ≅ Δ OMX ∴ RX = MX Since RX = MX So, OX bisects chord RM, ∴ OX ⊥ RM Now, Let OX = x, So, XS = OS – OX = 5 – x From (3) & (4) 25 – x2 = 11 – x2 + 10x 25 – 11 – x2 + x2 = 10x 14 = 10x 10x = 14 x = 14/10 x = 1.4 Putting value of x in (3) RX2 = 25 – x2 RX2 = 25 – (1.4)2 RX2 = 25 – 1.96 RX2 = 23.04 RX = √("23.04" ) RX = 4.8 Therefore, RM = 2RX = 2 × 4.8 = 9.6 m ∴ Distance between Reshma and Mandip is 9.6 m

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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