Question

Square ABCD has center O and AB = 900. Points E and F are on the side AB with AE < BF and E between A and F. If ∠EOF = 45° and EF = 400, then find BF.

Answer 1

we have given EF = 400
E between A and F
therefore AE = 400
AB = 900
Therefore
BF = AB - AE - EF

Answer 2

Let us suppose M is the mid point of side AB.
Since O is the centre of square therefore OM = 900/2 = 450 unit.Let <EOM = x and <FOM = y such that x+y = 45
Therefore, EM = 450 tan x and MF = 450 tan y Also, 450 [tan x + tan y] = 400 => tan x + tan y = 8/9
Given thant x + y = 45 => tan x + tan (45-x) = 8/9 => 9tan^2 x -8 tan x + 1 = 0 ......(1)

Solving (1) you will get , tan x = 4+SQRT(7)/9 & tan y = 4-SQRT(7)/9.
Therefore ,

BF = BM- MF = 450 - 450 tan y = 250 + 50 SQRT(7).

Answer 3

why are u taking it so difficult?