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ABC is a triangle right-angled at B. The...

ABC is a triangle right-angled at B. The hypotenuse (AC) is four the perpendicular (BD) drawn to it from the opposite vertex AD `lt` DC.
What is AD : DC equal to ?

A

`(7 - 2 sqrt(3)) : 1`

B

`(7 - 4 sqrt(3)) : 1`

C

`1 : 2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`AD : DC=(AD)/(DC)=(P(2-sqrt(3)))/(P(2+sqrt(3)))=(2-sqrt(3))/(2+sqrt(3))xx(2-sqrt(3))/(2-sqrt(3))`
`=(4+3-4sqrt(3))/(1)=(7-4 sqrt(3))/(1)`
`therefore AD : DC = 7 - 4 sqrt(3) : 1`
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