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
Read Solution (Total 2)
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- a.equilateral
eg if we take 6 as a side of triange a=6,b=6,c=6
then lhs=6^2+6^2+6^2=108
and rhs=6*6+6*6+6*6=108
lhs=rhs - 12 years agoHelpfull: Yes(3) No(0)
- a.equilateral
say each side is x units.
then
a^2+b^2+c^2 = 3x^2
bc+ca+ab = 3x^2
hence
a^2+b^2+c^2 = bc+ca+ab
- 12 years agoHelpfull: Yes(3) No(0)
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