Ex 10.4, 6 - A circular park of radius 20 m is situated - Ex 10.4

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  1. Chapter 10 Class 9 Circles
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Ex 10.4, 6 A circular park of radius 20 m 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. Given: Circular park with radius 20m Let Ankur, Syed and David be donated by points A,S & D resp. Given all three are sitting at equal distances, i.e., AS = SD = AD To find: Length of AS = SD = AD Explanation: Let AS = SD = AD = 2x In ASD, all sides are equal, โˆด ASD is an equilateral triangle We draw OP โŠฅ SD So, SP = DP = 1/2 SD โ‡’ SP = DP = 2๐‘ฅ/2 = x Join OS & AO In ฮ” OPS By Pythagoras theorem OS2 = OP2 + PS2 (20)2 = OP2 + x2 400 = OP2 + x2 400 โ€“ x2 = OP2 OP2 = 400 โ€“ x2 OP = โˆš("400 โ€“ x2" ) Now, AP = AO + OP โˆš("3" )x = 20 + โˆš("400 โ€“ x2" ) โˆš("3" )x โ€“ 20 = โˆš("400 โ€“ x2" ) โˆš("400 โ€“ x2" ) = โˆš("3" )x โ€“ 20 Squaring both sides (โˆš("400 โ€“ x2" ))^2= (โˆš("3" )x โ€“ 20)2 400 โ€“ x2 = (โˆš3x)2 + (20)2 โ€“ 2 ร—(โˆš3x) ร— (20) "400 โ€“ x2 =" 3x2 + 400 โ€“ 40โˆš3x "400 โ€“ 400 + 40" โˆš3 "x =" 3x2 + x2 "40" โˆš3 "x =" 4x2 4x2 = 40โˆš3x "x2" /"x" = 40/4 โˆš3 x = 10โˆš3 m AS = SD = AD = 2x = 2 ร— 10โˆš3 = 20โˆš3 m โˆด Length of string of each phone is 20โˆš3 m

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