Correct: #8, #9, #11, #12, #13, #14
Had trouble / wrong: #10, #15
Reflection / What happened:
#10 – Tried using no trig (just similar triangles + Ptolemy). Computations got messy, and I wasn’t fully confident the setup was correct.
#15 – I got pretty far into the official solution, but the step right before multiplying by Σi=1n(1-ai) didn’t feel motivated to me at first (why multiply by that?). It makes more sense now, but I need to see this trick more often.
Notes:
• Cauchy–Schwarz is the right tool here and the method is clean, but it’s very tricky in execution.
• I understand the solution after reading it, but I need more problems like this to become consistent.
Had trouble / wrong: #10, #15
Reflection / What happened:
#10 – Tried using no trig (just similar triangles + Ptolemy). Computations got messy, and I wasn’t fully confident the setup was correct.
#15 – I got pretty far into the official solution, but the step right before multiplying by Σi=1n(1-ai) didn’t feel motivated to me at first (why multiply by that?). It makes more sense now, but I need to see this trick more often.
Notes:
• Cauchy–Schwarz is the right tool here and the method is clean, but it’s very tricky in execution.
• I understand the solution after reading it, but I need more problems like this to become consistent.
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