Is the ABC an obtuse-angled triangle? 1) Two vertices A and B of AB

Question

Is the ∆ABC an obtuse-angled triangle?

1) Two vertices A and B of ∆ABC are on the circumference of a circle P, and the third vertex is inside the circle P
2) AB is the longest chord in circle P

Source: https://www.GMATinsight.com

GT1944 · Answer

for obtuse angle triangle a^2+b^2 < c^2

St 1: triangle could of any type e.g. a right triangle or an acute angled or an obtuse angled so insufficient

St 2: third vertex information is missing so insufficient

St 1+2
two vertext at diameter and third inside circle i.e. angle at third vertext > 90
sufficient

IMO C

Archit3110 · Answer

Target of question:
For triangle abc is obtuse ; i.e 
Obtuse angle is when one of angles of the ∆ is between 90<*<180
#1
Two vertices A and B of ∆ABC are on the circumference of a circle P, and the third vertex is inside the circle P
With given info we cannot determine at which points do vertices a,b lie on the circumfernce and also location of vertice C is not know 
insufficient 
#2
AB is the longest chord in circle P
AB longest chord is diameter , but no info about third point C as if its on circumference then it would be right angled else if inside circle then its obtuse ∆
insufficient 
From 1&2
We can say that AB is diameter such that its side ab is greatest and vertex c lies inside circle , hence its an obtuse ∆
sufficient 
OPTION C

Is the ABC an obtuse-angled triangle? 1) Two vertices A and B of AB

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