Find the length of x .

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AOB is a quarter circle, DE = x , BE = 4 and AD = OD .
Find the length of x .

Cherish Math

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i found a demonstration: what do you think of it ?
we have 3 equations with 3 unknown factors, with y=(EB]
x^2+y^2=5/4*r^2, [r*(5^1/2)/2+x]^2+y^2=4r^2, 1/2=y/ [r*(5^1/2)/2+x]
finaly we have x=3r/(2*5^1/2) and y=2r/5^1/2 and x=y*3/4, so if y=4 x=3.

claudelebourlegat

hey Cherish Math, what do you think ?, are you ok with this ?

claudelebourlegat

how do you proove that EDC are aligned ?

claudelebourlegat

Join DB so In Triangle DEB DB =(x square +4square)^1/2
And in Triangle DOB
R^2+R^2=(x^2+4^2)^1/2
We know DOB is right angled triangle so
Tan teta=R/2)/R=1/2=
So now
Cos Teta =R/(x^2+4^2)^1/2
We also know Teta
Two equation and two variable of R and X

bhriguvats