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Question

# In a right angled △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of △ABD and △ BCD?

A

(ABBC)2

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B

(ABAC)2

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C

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D

(BDDC)2

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Solution

## The correct option is B (ABAC)2 Consider △ABD and △BCD: Since, in △BDC, ∠DBC=90∘−∠C=∠A and in △ABC,∠A=90∘−∠C, ⇒∠BAD=∠DBC and ∠BDA=∠BDC [90∘] By AA similarity criterion, △ADB∼△BDC Hence, Ar(ΔABD)Ar(ΔBDC)=(ABBC)2=(ADBD)2=(BDDC)2 Thus, the option (ABAC)2 is required answer.

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