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# Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC

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Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC  [#permalink]

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15 Jan 2019, 22:23
1
1
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Difficulty:

55% (hard)

Question Stats:

51% (01:31) correct 49% (01:06) wrong based on 52 sessions

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Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC which are the two equal sides?

(1) Exterior angle at B is acute.

(2) Exterior angle at A is obtuse.
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Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC  [#permalink]

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Updated on: 17 Jan 2019, 01:26
amanvermagmat wrote:
Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC which are the two equal sides?

(1) Exterior angle at B is acute.

(2) Exterior angle at A is obtuse.

#1
for an isosceles triangle the two interior angles are equal and third angle >90 ; eg 45:45;90
given
Exterior angle at B is acute but not sure of other two sides would have exterior angle as obtuse and interior as acute so sufficeint ; as its given that triangle is isosceles..
sufficient

#2:
angle a interal angle <90 ; which all other internal angles may or may not be <90 not clear ; insufficient
IMO A

Originally posted by Archit3110 on 16 Jan 2019, 02:24.
Last edited by Archit3110 on 17 Jan 2019, 01:26, edited 1 time in total.
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Re: Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC  [#permalink]

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16 Jan 2019, 12:47
amanvermagmat wrote:
Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC which are the two equal sides?

(1) Exterior angle at B is acute.

(2) Exterior angle at A is obtuse.

Draw triangle ABC. Draw line segments jutting out from vertices A and B to form external angles. Label the internal angles as x,y,z as below
Attachments

Untitled.png [ 19.86 KiB | Viewed 498 times ]

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Re: Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC  [#permalink]

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16 Jan 2019, 20:44
In a Triangle , there can be only one Obtuse angle.
If one angle is >90 (obtuse), then the other two angles has to be acute (<90) since sum of all the angles in the triangle is 180.
Statement 1: exterior angle at B is acute. Hence Angle B, is obtuse. If angle B is obtuse, the other two angles A and B are acute. Since it is an Isosceles triangle, Angle A= Angle B , and sides opposite to these two angles are equal. hence Sufficient.
Statement 2: This statement tells that Angle A is acute ie, Angle A <90. Angle B as well as angle C can also be acute. We do not know which two angles are equal. Hence Insufficient.
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Re: Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC  [#permalink]

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17 Jan 2019, 06:41
Sum of 3 angles = 180in triangle
ANd sum of 2 interior angle is eqaul to exterior angle of remaining side
So,
(1) Exterior angle at B is acute.
So , angle B is obtuse >90
This gives us sum of angle A+C= <90=Ext angle B
so this case is only possible when angle side opposite to a and c are eqaul

(2) Exterior angle at A is obtuse.
interior angle a <90

Thanks
Re: Triangle ABC is isosceles but not equilateral. Out of AB, BC and AC   [#permalink] 17 Jan 2019, 06:41
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