CAT Exam

If a, b and c are the sides of a triangle, and a^2+b^2+c^2 = bc+ca+ab, then the triangle is
a.equilateral b.isosceles c.right-angled d.obtuse-angled

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CAT Other Question

Consider a circle with unit radius. There are seven adjacent sectors, S1,S2,S3, ..., S7, in the circle such that their total area is 1/8 of the area of the circle. Further, the area of the jth sector is twice that of the (j–1)th sector, for j = 2, ..., 7. What is the angle, in radians, subtended by the arc of S1
at the centre of the circle?

A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, 3 km north of the north gate, and it can just be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city?
a.6 km b.9 km c.12 km d.None of these