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

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

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New post 06 Aug 2018, 10:27
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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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Triangle ABC is equilateral. A point D lies on side BC and AD is  [#permalink]

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New post 06 Aug 2018, 11:05
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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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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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Triangle ABC is equilateral. A point D lies on side BC and AD is

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