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Question

# △ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. If AD: DC = 1:2, then AB2BC2 is:

A

1: 2

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B

1: 4

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C

4: 1

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D

2: 1

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Solution

## The correct option is A 1: 2 Consider △ADB and △ABC ∠BAD = ∠BAC [common angle] ∠BDA = ∠ABC [ 90∘] Therefore by AA similarity criterion, △ADB and △ABC are similar. So, ABAC = ADAB ⇒ AB2 = AC . AD -------------(I) Similarly, △BDC and △ABC are similar. So, BCAC = DCBC ⇒ BC2 = AC . DC -------------(II) Dividing (I) and (II) and cancelling out AC, we get, (ABBC)2 = ADDC -------------(III) So, the ratio is the same, i.e., 1: 2.

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