Submitted by Grainne on Mon, 07/24/2017 - 14:13
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Hey, I've been struggling to work out the proof for assignment 4 question 1 part 2. I got the first part and the rest of the assignment already but I just can't work this one out. Thanks for any help
Q1 (ii)
Start by drawing a diagram, and you should find that the lines $AP$ and $OB$ cross (or $BP$ and $OA$ depending on your diagram).
Add in a line $OP$. We then have triangles $AOP$ and $BOP$ which are both isosceles. We have:
\[
\angle{OAP}=\angle{OPA}=x \\
\angle{OBP}=\angle{OPB}=y
\]
From here you should be able to write $\angle {APB}$ and $\angle {AOB}$ in terms of $x$ and $y$.
I also struggled until I went
I also struggled until I went back to my part i) diagram and redrew it with the same letters and x and y but with just P shifted around until O was outside the ABP triangle. Then it was a case of using the same method as in the first part.