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ABC is a right angled triangle such that AB = a - b, BC = a and CA = a + b. D is a point on BC such that BD = AB. The ratio of BD : DC for any value of a and b is given by

A) 3 ; 2
B) 4 : 3
C) 5 : 4
D) 3 : 1

Correct Answer:




D) 3 : 1

Description for Correct answer:
In right angled \( \Large \triangle ABC \)

\( \Large \left(a+b\right)^{2}= \left(a-b\right)^{2}+a^{2} \)

=> \( \Large a^{2}+b^{2}+2ab = a^{2}+b^{2}-2ab+a^{2} \)

=> \( \Large 4ab = a^{2} => 4b = a \)

Now, \( \Large \frac{BD}{DC}=\frac{a-b}{b}=\frac{4b-b}{b} \)

= \( \Large \frac{3b}{b} = \frac{3}{1} \)

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

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