[paperclip345]

Can someone help me with part b) of this question? I worked out that angle PBC = 80 (which is pretty easy) but I'm totally lost with where you go from there

[TenOfThem]

Either use the alternate segment theorem

OR

draw a line from B to the centre and use what you know about tangent and radius angles

[tamimi]

Let O be the centre of the circle.
Join BO and CO.

As triangles ABP and ACP are congruent, angle CPA = 10 deg.
Angle BPC = angle BPA + angle CPA = 20 deg.

In quadrilateral OBPC:
Angle OBP = 90 deg (tangent perpendicular to radius)
Angle OCP = 90 deg (tangent perpendicular to radius)

Therefore OBPC is cyclic (opposite angles supplementary)
Anlge BOC = 180 deg - angle BPC
= 180 - 20
= 160 deg.

Angle BAC = angle BOC / 2
= 80 deg. (angle at the centre is twice that at the circumference)

In triangle ABC, therefore, as angle ABC = angle BCA:
Angle ABC = (1 / 2)(180 - angle BAC)
= (1 / 2)(180 - 80)
= 50 deg.

[TenOfThem]

(Original post by tamimi)
...

http://www.thestudentroom.co.uk/showthread.php?t=403989

The guidelines are quite clear regarding the posting of full solutions

[paperclip345]

Thank you so much, I understand it now

[notnek]

(Original post by TenOfThem)
Either use the alternate segment theorem

Can the alternate segment theorem be quoted in a GCSE exam? I don't remember ever doing a GCSE exam question where it came up and I'm not even sure I was taught it.

I'm currently more used to the IGCSE where it is not taught and it's been too long since I studied GCSE.

If it is allowed, then the OP's question becomes quite easy.

[TenOfThem]

(Original post by notnek)
Can the alternate segment theorem be quoted in a GCSE exam? I don't remember ever doing a GCSE exam question where it came up and I'm not even sure I was taught it.

It is certainly in the AQA GCSE

[mia_hilton]

Hi guys, how can i learn the proof of each of the circle theorems it's something i'm really struggling with ...help please!

[krisshP]

(Original post by mia_hilton)
Hi guys, how can i learn the proof of each of the circle theorems it's something i'm really struggling with ...help please!

I'm doing the same as you right now. Just keep on practising and make sure after each question you finish you have EXPLAINED why you received your answer.

[TenOfThem]

(Original post by mia_hilton)
Hi guys, how can i learn the proof of each of the circle theorems it's something i'm really struggling with ...help please!

Which board are you doing that requires the proofs?

[mia_hilton]

(Original post by TenOfThem)
Which board are you doing that requires the proofs?

[COLOR="#0000CD"]Edexcel the 1MAO/1H paper - we were taught the profs but i missed the lesson - so i think we may have to know the proofs?

[TenOfThem]

WoW ... AQA requires no such proof

So, these are the ones that you need to prove

prove and use the facts that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference
the angle subtended at the circumference by a semicircle is a right angle
that angles in the same segment are equal
and that opposite angles of a cyclic quadrilateral sum to 180 degrees
prove and use the alternate segment theorem

The standard proofs are probably in your textbook ... is it that you cannot find them or that you do not understand them

[notnek]

(Original post by TenOfThem)
WoW ... AQA requires no such proof

So, these are the ones that you need to prove

prove and use the facts that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference
the angle subtended at the circumference by a semicircle is a right angle
that angles in the same segment are equal
and that opposite angles of a cyclic quadrilateral sum to 180 degrees
prove and use the alternate segment theorem

The standard proofs are probably in your textbook ... is it that you cannot find them or that you do not understand them

We still don't know if the exam board requires the proofs. I think it's more likely that the teacher showed the proofs (as I do) to the class but the proofs are not actually in the syllabus.

I would check the syllabus but my internet is too slow.

[TenOfThem]

(Original post by notnek)
We still don't know if the exam board requires the proofs. I think it's more likely that the teacher showed the proofs (as I do) to the class but the proofs are not actually in the syllabus.

I would check the syllabus but my internet is too slow.

My italics are from the syllabus

[notnek]

(Original post by TenOfThem)
My italics are from the syllabus

OK then I share your Wow.