Need help with this circle theorem question

This is my current answer

BCD=x
BOD=2x
this is because the angle in the center is 2 times the angle at the circumfrence
ODA=90
ODA=OBA
because the angle between the tangent and the gradient is 90
ODA+OBA=180
360-(2x+180)
because angles in a quadrilateral add up to 360
so angle BAD=360-(2x+90+90)
BAD=360-180-2x
BAD=180˚-2x˚
BAD=90˚-x˚
 
How can BAD = both 180-2x and 90-x. If a number = a multiple of itself then the number is 0.

That is if 180-2x = 2*(90-x) = 90-x, then 90-x=0. Hence x=90. Is this the correct answer?
 
The inscribed \(\angle BCD\) has measure \(x\) therefore \(m(\angle BOD)=2x\).
So \(m(\widehat{BD}=2x\) that means \(m(\angle BAD)=\frac{1}{2}\left(\widehat{BCD}-\widehat{BD}\right)\) Why and HOW?
Moreover \(m(\angle BAD)+2\left(\frac{\pi}{2}\right)+2x=2\pi\).
Can you finish?
 
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