F.5 MATH&@#%$#&(
2010-11-08 4:38 am
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The inscribed circle of ΔABC is a unit circle. AB=AC, AD⊥BC. E is the centre of the circle. BE bisects ∠ABC. Let AD = h and BD = r.
(a) By using the formula for tan2θ, or otherwise, prove that h = 2(r^2) / [(r^2) - 1]. Hence deduce that r^2 = h / (h-2).
回答 (1)
2010-11-08 10:36 am
✔ 最佳答案
a)Let θ be ∠EBD = ∠ABE.AD / BD = h / rtan ∠ ABD = h / rtan 2θ = h / r(2 tanθ) / (1 - tan²θ) = h / rSince tanθ = ED / BD = 1 / r ,(2/r) / (1 - 1/r²) = h / r2 / (1 - 1/r²) = hh = 2r² / (r² - 1)Sohr² - h = 2r²r² (h - 2) = hr² = h / (h - 2)
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