The Last Question from the Senior Maths Challenge | Math Olympiad Training

Can you solve this geometry problem from the U.K Maths Olympiad?

This problem comes from the 2018 Senior Maths Challenge in the U.K for 17/18-year-old students.

Did you solve it?
Let me know in the comments how you solved this problem. I’d love to hear about it!

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Maths videos by Giuliano Grasso - mathematics graduate from the University of East Anglia.

I post weekly maths olympiad videos for you to try and solve.

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[wetasspaddington]

how do u prove that OP is the same as the diameter of the semicircle? is that just assumed it seems a little random?

[dawoudalam]

see this proof is true, but from the diagram you can just guess it tto be 2/3 as all the other options are simply ruled out when u think about the relative area