fiza gupta wrote:If points A, B, and C form a triangle, is angle ABC > 90 degrees?
(1) AC = AB + BC − 0.001
(2) AC = AB

OA:B

We have to ensure whether angle B > 90.

S1:

AC = AB + BC − 0.001 implies that AC > AB + BC;

This is possible in following scenerios.

1. If AC > AB and AC > BC, then the angle opposite the greatest side AC, i.e., angle B can be the greatest and have a value greater than 90. Answer is YES.

2. However, if AC is not be the greatest side. For example, AC = AB = BC = 0.001, then the triangle will be equilateral, thus each of its angles will be 60. Answer is NO.

No unique answer.

S2:

AC = AB implies that and angle B = angle C.

Say, angle B = angle C = x.

=> Angle A = 180 - x - x = 180 - 2x

We know that angle A > 0

=> 180 - 2x > 0 => x < 90

Angle ABC < 90. The answer is NO. Sufficient

OA: B

-Jay
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