Solving Congruent Triangles Inscribed in a Circle

[thomas49th]

Sorry, it's upside down :(

How do i go about solving A. I know that for somthing to be congruent it needs to

SSS
RHS
AAS
SAS

I know that C = B because they lie on a circuference and a chord that binds them is A. Where do I go from now?

Thx

 

[cristo]

I know that for somthing to be congruent it needs to

SSS
RHS
AAS
SAS

What does this mean?

 

[thomas49th]

abreivations of triangle congruency

take a look:
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeh/congruencyandsimilarityrev2.shtml

 

[chaoseverlasting]

Angles pcb and pbc are also equal (alternate angle theorem). Therefore, pc=pb (sides opp equal angles). This gives you two sides equal and 1 side common so sss congruency is established.

 

[thomas49th]

I don't see how it's alternate segment theory...

The angle between a tangent and a chord is equal to the angle made by that chord in the alternate segment.

I can't see it. Do you know a good technique for spotting it?

Thx

 

[chaoseverlasting]

If you extend pc to some point, say q. Then angle acq is equal to angle abc. Apply the same thing on the other side of the quad.

 

[bharata]

OKay, this is my thinking
statement 1: AP=AP Reason: common line (S)
statement 2: <ABC = <ACB reason: given
statement 3: <PBC = <PCB reason: tangent from the same point P
statement 4: therefore <ABP = <ACP reason: see statement 2&3 (A)
statement 5: <CPA = <BPA reason: tangent cords are from the same point P (A)
statement 6: triangle ABP = triangle ACP reason: AAS

but I'm not sure for statement 5, as the diagram doesn't indicate anything...