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VTMO 2026 - Grade 7 - Semifinal - SET 1 - Self-study Question 12

VTMO · VTMO 2026 - Grade 7 - Semifinal - SET 1 - Self-study

Question 12

Given $\frac{a+b}{2c}=\frac{a-b}{2d}=\frac{c+d}{2a}=\frac{c-d}{2b}$, calculate
$$S=\frac{(a+b)^2-(a-b)^2+(c+d)^2-(c-d)^2}{a^2-b^2+c^2-d^2}.$$

Question illustration