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# DS - Geometry

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Manager
Joined: 12 Apr 2006
Posts: 210
Location: India

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24 Jun 2009, 03:49
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Current Student
Joined: 03 Aug 2006
Posts: 112

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24 Jun 2009, 10:31
1
KUDOS

From the figure:

$$\angle BDC = 2x$$

$$\Rightarrow \angle BDA = 180 - 2x$$

Also

$$\angle BAD = x$$

$$then \angle ABD = 180 - \angle BDA - \angle BAD = 180 - (180-2x) - x = 180-180+2x-x = x$$

$$as \angle BAD = \angle ABD$$

This make $$\triangle ABD$$ an isosceles triangle

hence

$$side (AD) = side (BD)$$ --- 1

Also

$$\angle BDC = \angle BCD = 2x$$

This make$$\triangle DBC$$ an isosceles triangle

Hence

$$side (BD) = side (BC)$$ --- 2

from 1 and 2

$$side (AD) = side (BD) = side (BC)$$

Hence we need length of $$side (AD)$$ or $$side (BD)$$ to get length of $$side (BC)$$

Looking at statement 1.

$$side(AD) = 6$$ ---- Sufficient

Looking at Statement 2

$$x = 36$$

this does not tell us anything about the lengths of $$side(AD)$$ or $$side(BD)$$ ---- Insufficient.
Re: DS - Geometry   [#permalink] 24 Jun 2009, 10:31
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