Question

find the value of EF
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Answer 1

Given :  a rectangle from center of circle  with dimensions

To find : Value of EF

Soluion:

Rectangle has sides  15  & 20

=> Diagonal length = BD = OC = √(15² + 20²) = 25

=> Radius of circle = OC = 25

BD = 25

let draw OM ⊥ EF  (or BD)

Let say DM  = x  then BM = 25 - x

then OM² = OD² - DM²

=> OM² = 15² - x²

=> OM² = 225 - x²

& OM² = OB² - BM²

=> OM² = 20² - (25 - x)²

=> OM² = 400 - ( 625 + x² - 50x)

=> OM² =  -225 - x² + 50x

225 - x² =  -225 - x² + 50x

=> 50x = 450

=> x = 9

OM² = 225 - 9²

=> OM² = 144

=>OM = 12

OM = 12   OE = OF = 25   ( Radius)

=> EM² = FM²  = 25² - 12²

=> EM = FM  = √481

=> EF = 2√481  = 43.86

EF = 2√481  = 43.86

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