A rode 8 kilometre long is constructed along the chord PQ of a circular path of radius 5 km to more roads are to be constructed from an external point P to the circle and tangential to it at P and Q is expenses are 12000 per kilometre for a construction the new roads TP and TQ find the total cost of the roads to be constructed
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see the attachement,
here we have to find PT and PQ
let see how to get,
∠POT = tan⁻¹ (4/3)
now for triangle Δ PTO,
tan(tan⁻¹(4/3)) = PT/5
⇒ 4/3 = PT/5
PT = 20/3 km
according to circle theorem,
PT = TQ = 20/3 km
so, cost of construction of PT = cost of construction of TQ = 12000 × 20/3
= 4000 × 20 = 80,000 Rs
so, total cost to construct TP and TQ = 2 × 80,000 = 1,60,000 Rs
here we have to find PT and PQ
let see how to get,
∠POT = tan⁻¹ (4/3)
now for triangle Δ PTO,
tan(tan⁻¹(4/3)) = PT/5
⇒ 4/3 = PT/5
PT = 20/3 km
according to circle theorem,
PT = TQ = 20/3 km
so, cost of construction of PT = cost of construction of TQ = 12000 × 20/3
= 4000 × 20 = 80,000 Rs
so, total cost to construct TP and TQ = 2 × 80,000 = 1,60,000 Rs
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