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 to each other. Find the length of the string of each phone.

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Let Ankur 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=90oBy Pythagoras theorem,AS2=AB2+BS2∴AB2=AS2−BS2=x2−(2x​)2=43x2​        ∴AB=23​x​ mNow, AB=AO+OBOB=AB−AOOB=(23​x​−20) mIn △OBS,OS2=OB2+SB2202=(23​x​−20)2+(2x​)2400=43​x2+400−2(20)(23​x​)+4x2​ 0=x2−203​x∴x=203​mThe length of the string of each phone is 203​m.

Question Text	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 to each other. Find the length of the string of each phone.
Answer Type	Text solution:1
Upvotes	150

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 to each other. Find the length of the string of each phone.

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