# Points on a circle.3

#### Mukilab

In the diagram attached a is the centre ogf the circle (O doesn't work in paint).
P,Q,R and S are points on the circle
Angle ROP = 110
Calculate the angle RSP

I Don't know how to prove it is a parallelogram (if it is (although I suspect it is)), I need names of laws and if there are specific names given to various angles (not like obtuse or acute but things like RSP is the intercept angle, although I know it's not but I don't know what the intercept angle is)

This is all GCSE standard, please do not venture further. #### Wilmer

This is all GCSE standard, please do not venture further.
WHAT does that mean?

Is angle PQR = 35 ?

#### Mukilab

No, 55, apologies for that.

I mean this is for my GCSEs and because I have never taken any maths classes I have to learn this all by myself within an incredibly small amount of time so I do not want people to elaborate because I will simply not remember the equations.

GCSEs are national exams in England.

#### masters

MHF Helper
In the diagram attached a is the centre ogf the circle (O doesn't work in paint).
P,Q,R and S are points on the circle
Angle ROP = 110
Calculate the angle RSP
Hi Mukilab,

Your drawing leaves something to be desired. If you're using Paint, take your time.

If angle ROP = 110, and if it is a central angle, then arc RSP is also 110 degrees.

That leaves 360 - 110 = 250 degrees for arc RQP (the rest of the circle).

Angle RSP is an inscribed angle that intercepts this arc, so
it is one-half its measure.

That makes Angle RSP = 1/2 (250) or 125 degrees.

I don't know what a parallelogram has to do with anything.

• Mukilab