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# Triangle ABC is equilateral. A point D lies on side BC and AD is

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Joined: 21 Aug 2013
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Triangle ABC is equilateral. A point D lies on side BC and AD is  [#permalink]

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06 Aug 2018, 10:27
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:07) correct 28% (01:34) wrong based on 29 sessions

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Triangle ABC is equilateral. A point D lies on side BC and AD is joined. Is the area of triangle ADB equal to that of triangle ADC?

(1) angle BAD < 30 degrees

(2) angle ADB > 90 degrees
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Status: Learning stage
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Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Triangle ABC is equilateral. A point D lies on side BC and AD is  [#permalink]

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06 Aug 2018, 11:05
2
amanvermagmat wrote:
Triangle ABC is equilateral. A point D lies on side BC and AD is joined. Is the area of triangle ADB equal to that of triangle ADC?

(1) angle BAD < 30 degrees

(2) angle ADB > 90 degrees

Area of $$\triangle{ADB}$$=$$\triangle{ADC}$$ s.t. following conditions
a) 'D' is the midpoint of side BC (BD=CD) Or, AD is the median of $$\triangle{ABC}$$
b) AD is the angle bisector($$\angle{BAD}$$=$$\angle{CAD}$$) or AD is the perpendicular bisector of BC ($$\angle{ADB}$$=$$\angle{ADC}$$)
Apart from above, in all other conditions, area won't be equal. In short, any trial of shifting point 'D' left or right on the side BC will lead to inequality in areas of two triangles.

St1:- $$\angle{BAD} < 30$$ degrees
Violates condition (a) and (b).
Hence area of triangles under discussion is not equal.
Sufficient.

St2:- $$\angle{ADB} > 90$$ degrees
Violates condition (a) and (b).
Hence area of triangles under discussion is not equal.
Sufficient.

Ans. (D)
.
P.S.:- Only in an equilateral triangle, the altitude, median, angle bisector, and perpendicular bisector for each side are all the same single line
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Regards,

PKN

Rise above the storm, you will find the sunshine

Triangle ABC is equilateral. A point D lies on side BC and AD is &nbs [#permalink] 06 Aug 2018, 11:05
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