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Home » But we want the ratio of the area of the incircle to the area of the triangle: - Sourci

But we want the ratio of the area of the incircle to the area of the triangle: - Sourci

📅 May 2, 2026 👤 scraface

May 02, 2026

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Question: Let $ a $ and $ b $ be complex numbers such that $ |a| = |b|...
eq b $. Find the value of $ rac{a + b}{a - b} + rac{a - b}{a + b} $.
Solution: Let $ S = rac{a + b}{a - b} + rac{a - b}{a + b} $. Combine...
S = rac{(a + b)^2 + (a - b)^2}{(a - b)(a + b)} = rac{2a^2 + 2b^2}{a^...
Since $ |a| = |b| = 1 $, $ a \overline{a} = 1 $ and $ b \overline{b} =...
S + \overline{S} = rac{(a + b)^2 + (a - b)^2}{a^2 - b^2} = rac{2a^2...
But $ a
eq b $, and $ |a| = |b| = 1 $. Let $ b = \overline{a} $ (since $ |a| =...
eq \overline{a} $ unless $ a $ is real, which contradicts $ a
eq b $. Instead, note that $ rac{a + b}{a - b} + rac{a - b}{a + b} =...

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