Triangle In Circle, Prove An Angle

The diagram doesn’t look accurate? Where did you get 180-2x from? The top vertice of the triangle is not vertically above the centre and how can OC be r? I’m really confused

Excuse my lack of ruler/ ability in drawing diagrams properly. I tend not to put in too much effort into diagrams unless I am doing an actual exam!

Have you encountered the fact that the angle at the centre of the circle is twice the angle at the circumference? From there, we are using the fact that AB is a straight line and so angle AOC+ angle COB = 180.

Reply 21

Radioactivedecay

16

Original post by Y11_Maths

Isn’t the area of the triangle r^2/2, or am I wrong?

No, the area of the triangle has x in there somewhere, else how are you going to figure out what x is?

Reply 22

Y2_UniMaths

OP

19

Original post by I hate maths

As I was saying to Notnek, it wouldn't require this as the question gives you the value of x, so you can sub it in and confirm it's the solution without knowledge of identities. People tend to have an aversion for this kind of solution but I think it's a useful way to do some problems.

I asked if you could substitute x as 15 degrees in and he said no, you have to prove that it is the final outcome not that everything else fits perfectly into place when that value is 15 degrees...

Reply 23

Y2_UniMaths

OP

19

Original post by psc---maths

Excuse my lack of ruler/ ability in drawing diagrams properly. I tend not to put in too much effort into diagrams unless I am doing an actual exam!

Have you encountered the fact that the angle at the centre of the circle is twice the angle at the circumference? From there, we are using the fact that AB is a straight line and so angle AOC+ angle COB = 180.

Yes I understand this but don’t know where you got your values from

Reply 24

Notnek

21

Original post by I hate maths

As I was saying to Notnek, it wouldn't require this as the question gives you the value of x, so you can sub it in and confirm it's the solution without knowledge of identities. People tend to have an aversion for this kind of solution but I think it's a useful way to do some problems.

This assumes it's a calculator question. The method given by @psc---maths is a bit nicer for GCSE since you can use sin(30) = 1/2. Although it relies on sin(2x) = sin(180-2x) which I wouldn't expect most GCSE students to realise.

If it was a calculator question then since it's a "show that", you could just set x as 15 and find the areas in terms of r.

Reply 25

username3555092

14

Original post by Y11_Maths

I asked if you could substitute x as 15 degrees in and he said no, you have to prove that it is the final outcome not that everything else fits perfectly into place when that value is 15 degrees...

I don't mean subbing x=15 straight away into the diagram and working with that throughout. It's fine to work with x's all the way through and get to the last stage where "expression in x"="something" and show that x=15 satisfies that condition, and that it's the only value which could satisfy that condition (in this case, it's not though). It's something to at least be aware of. Psc's diagram will provide a nice direct method, and probably the way your teacher wants you to approach the problem, so I'd go with that certainly.

EDIT: @Notnek you're completely right, I assumed this is a calculator question. Forgot non-calculator GCSE papers are a thing... My bad.

(edited 6 years ago)

Reply 26

Daveboi115

19

I’m woeful at maths, and I have no idea what any of this means or what any of you are saying. Nonetheless I’ve read the whole thing!

Reply 27

the bear

20

angle COB = 2x

the area of triangle ABC = r²/2

the area of triangle OBC = 1/2 of the area of triangle ABC

====> r²/4 = 1/2*OB*OC*Sin2x

etc.

Reply 28

Y2_UniMaths

OP

19

Original post by psc---maths

Excuse my lack of ruler/ ability in drawing diagrams properly. I tend not to put in too much effort into diagrams unless I am doing an actual exam!

Have you encountered the fact that the angle at the centre of the circle is twice the angle at the circumference? From there, we are using the fact that AB is a straight line and so angle AOC+ angle COB = 180.