Circle Theorem Problem

[Toby.tc]

Please can someone help me solve this using no more than GCSE level circle theorems?

 

[Deleted member 4993]

Please can someone help me solve this using no more than GCSE level circle theorems?

Please share your thoughts/work with us and tell us exactly where you are stuck!!

 

[Toby.tc]

Please share your thoughts/work with us and tell us exactly where you are stuck!!

I don’t understand where to begin, I tried to draw in some radii from a centre O but I got no where. I need to solve for m and n.

 

[Deleted member 4993]

I don’t understand where to begin, I tried to draw in some radii from a centre O but I got no where. I need to solve for m and n.

First label all the vertices. Show us the labeled sketch. Think about the exterior/interior angles of triangles also.

 

[Toby.tc]

First label all the vertices. Show us the labeled sketch. Think about the exterior/interior angles of triangles also.

I did it. Just needed a bit of thinking. Here’s the proof with enhanced diagram of added letters:

 

[pka]

Please can someone help me solve this using no more than GCSE level circle theorems?

@Toby, You should have followed S.Kann's suggestion to label the vertices.
So start and label the vertices on the circle: \(m(\angle A)=15^o\).
Now going clockwise \(B,~C,~D\). Then \(m(\angle E)=20^o~\&~m(\angle F)=u^o\).
By the inscribed angle theorem we know \(m(\widehat{CD})=30^o\).
We also know that \(20^o=\frac{1}{2}\left(m(\widehat{AB})-m(\widehat{CD})\right)\). Which gives \(m(\widehat{AB})\).
Now can you continue?

 

[Toby.tc]

@Toby, You should have followed S.Kann's suggestion to label the vertices.
So start and label the vertices on the circle: \(m(\angle A)=15^o\).
Now going clockwise \(B,~C,~D\). Then \(m(\angle E)=20^o~\&~m(\angle F)=u^o\).
By the inscribed angle theorem we know \(m(\widehat{CD})=30^o\).
We also know that \(20^o=\frac{1}{2}\left(m(\widehat{AB})-m(\widehat{CD})\right)\). Which gives \(m(\widehat{AB})\).
Now can you continue?

I’ve already completed the solution, but I can’t see how inscribed circle theorem is applicable as vertices E is not on the circumference. (Unless you are referring to an alternate perspective I haven’t seen). Thanks for the prompts, I’ll make sure to label my vertices next time.