Mathematics Geometry Circle Tangent Problem please help

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Harveybishop
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#1
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I am not sure how to find angle x. Would you draw a centre point to create triangle OBC, where O is the centre. The line OB is the radius of the triangle. The angle at C would equal to 20 degrees. The angle at B would be equal to 90 degrees, because of circle theorem 5.
Adding these; 90+20= 110
O = 70 degrees
Then according to circle theorem 1 'The angle at the centre is twice the angle at the circumference' so angle x would be half of O= 35 degrees.
I am unsure if this is right or not, I do not have much experience with circle theorems so any clarity or advice would be much appreciated.
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Harveybishop
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username1732133
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(Original post by Harveybishop)
I am not sure how to find angle x. Would you draw a centre point to create triangle OBC, where O is the centre. The line OB is the radius of the triangle. The angle at C would equal to 20 degrees. The angle at B would be equal to 90 degrees, because of circle theorem 5.
Adding these; 90+20= 110
O = 70 degrees
Then according to circle theorem 1 'The angle at the centre is twice the angle at the circumference' so angle x would be half of O= 35 degrees.
I am unsure if this is right or not, I do not have much experience with circle theorems so any clarity or advice would be much appreciated.
Your method is not quite correct. Your angle BOC = 70 degrees. x is not half of this angle. It is half of angle BOD.

A method that you might find easier is to draw BD and think about the isosceles triangle BCD and then use the alternate segment theorem.
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thekidwhogames
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Try putting a centre and linking it to B/D and use the theorem that those lines are perpendicular. Then use that kite to find the angle of O and thus x.
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astro-hannah
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does this help?
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Harveybishop
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(Original post by astro-hannah)
does this help?
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astro-hannah Yes it does, thank you very much 😊
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astro-hannah
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(Original post by Harveybishop)
astro-hannah Yes it does, thank you very much 😊
Yay! No probs
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Notnek
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#8
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I'm sure this exact question/image was posted a few weeks ago...
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