In the figure given below, if AB ∶ BC = 4 ∶ 5, then find the ratio AD ∶ AB.

F1 V.G D.K 10.08.2019 D7

  1. 2 ∶ 1
  2. 3 ∶ 2
  3. 4 ∶ 3
  4. 5 ∶ 4

Answer (Detailed Solution Below)

Option 2 : 3 ∶ 2
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Detailed Solution

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Given, AB ∶ BC = 4 ∶ 5

⇒ BC = (5/4) × AB

∵ AC = AB + BC

⇒ AC = AB + (5/4) × AB = (9/4) × AB

Applying the tangent-secant theorem, the tangent and the secant are related as,

⇒ AD2 = AB × AC

⇒ AD2 = (9/4) × AB2

⇒ AD/AB = √(9/4) = 3/2

∴ AD ∶ AB = 3 ∶ 2
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