Practice variation 3 of 3
Vectors — Area formula and numerical check, then maximise
Your question
(i) Show that the area of with , is , and verify with , .
(ii) Hence, for arising as the area factor for the double-angle circle configuration of the exam, find all that maximise when (equivalently maximise the triangle area).
This practice question was inspired by Question 14(c) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?