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A circular park of radius 20m is situated in a colony.Three boys Ankur,syed and david are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. find the length of the string of each phone.​

Answer»

ur be represented as A, Syed as S and David as D.The boys are sitting at an equal distance.Hence, △ASD is an equilateral triangle.Let the radius of the circular park be r meters.∴OS=r=20m.Let the length of each side of △ASD be x meters.Draw AB⊥SD∴SB=BD= 21 SD= 2x mIn △ABS,∠B=90 o By Pythagoras theorem,AS 2 =AB 2 +BS 2 ∴AB 2 =AS 2 −BS 2 =x 2 −( 2x ) 2 = 43x 2 ∴AB= 23 x mNow, AB=AO+OBOB=AB−AOOB=( 23 x −20) mIn △OBS,OS 2 =OB 2 +SB 2 20 2 =( 23 x −20) 2 +( 2x ) 2 400= 43 x 2 +400−2(20)( 23 x )+ 4x 2 0=x 2 −20 3 x∴x=20 3 MTHE length of the string of each phone is 20 3 m.solution


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