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If four sides of a quadrilateral ABCD are tangential to a circle, then 

A. AC + AD = BD + CD 

B. AB + CD = BC + AD 

C. AB + CD = AC + BC 

D. AC + AD = BC + DB

1 Answer

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Best answer

Answer is A. AC + AD = BD + CD

Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal. 

By the above property, 

AP = AS (tangent from A) 

BP = BQ (tangent from B) 

CR = CQ (tangent from C) 

DR = DS (tangent from D)

Now we add above 4 equations, 

AP + BP + CR + DR = AS + BQ + CQ + DS 

⇒ AB + CD = AD + BC 

[∵ AP + BP = AB 

CR + DR = CD 

AS + DS = AD 

BQ + CQ = BC] 

Hence, the right option is AB + CD = AD + BC

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