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In a ∆ ABC, AB = AC. A circle through B touches AC at D and intersects AB at P. If D is the mid-point of AC, which one of the following is correct? 

(a) AB = 2AP 

(b) AB = 3AP 

(c) AB = 4AP 

(d) 2AB = 5AP

1 Answer

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Best answer

Answer : (c) AB = 4AP

Using the tangent-secant theorem, we have 

AB × AP = AD2\(\big(\frac{AC}{2}\big)^2\)  ( ∵ AD = DC) 

⇒ AB × AP = \(\frac{1}{4}\) AC2 = \(\frac{1}{4}\) AB2 ( ∵ AB = AC) 

AB = 4 AP

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