Question-156913

Question Number 156913 by cortano last updated on 17/Oct/21

Answered by mr W last updated on 17/Oct/21

Commented by cortano last updated on 17/Oct/21

b l u e l e n g t h = 10 . y e s t h a n k s

Commented by mr W last updated on 17/Oct/21

O D = \sqrt{{(R - r)}^{2} - r^{2}} = \sqrt{R (R - 2 r)}

F D = R + \sqrt{R (R - 2 r)} = b l u e

O E = O D - r = \sqrt{R (R - 2 r)} - r

E G = R - O E

F E = R + O E

{A E}^{2} = F E \times E G = R^{2} - {O E}^{2}

{F A}^{2} = {A E}^{2} + {F E}^{2} = R^{2} - {O E}^{2} + {F E}^{2}

{F A}^{2} = R^{2} - {O E}^{2} + {(R + O E)}^{2}

{F A}^{2} = 2 R^{2} + 2 R \times O E

{F A}^{2} = 2 R^{2} + 2 R \times [\sqrt{R (R - 2 r)} - r]

{F A}^{2} = R^{2} + 2 R \sqrt{R (R - 2 r)} + R (R - 2 r)

{F A}^{2} = {[R + \sqrt{R (R - 2 r)}]}^{2}

F A = R + \sqrt{R (R - 2 r)} = g r e e

i t i s t o s e e F D = F A, i . e . b l u e = g r e e n .

Commented by Tawa11 last updated on 17/Oct/21

great sir

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