Let ABC be a triangle inscribed in a circle of radius r and A B = A C and h is the altitude from A to BC , then ( P = perimeter of △ A BC , △ = area)

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BC = 2 B D = 2 r 2 − ( h − r ) 2 ​ = 2 2 h r − h 2 ​ and A B = 2 h r ​ , so P = 2 A B + BC = 2 [ 2 h r − h 2 ​ + 2 h r ​ ] ​ Δ = B D × A D = h 2 h r − h 2 ​ ​ P 3 Δ ​ = 8 ( 2 h r − h 2 ​ + 2 h r ​ ) 3 h 2 h r − h 2 ​ ​ ⇒ h → 0 lim ​ P 3 Δ ​ = 128 r 1 ​ ​

Mathematics - Properties of Triangle Question with Solution | TestHub

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