Four points A,B,C and D lie on a straight line in X-Y plane,such that AB=BC=CD and length of AB is 1 metre.An?

Question

Four points A,B,C and D lie on a straight line in X-Y plane,such that AB=BC=CD and length of AB is 1 metre.An ant at A wants to reach a sugar particle at D.But there are insect repellentskept at points B and C.The ant would not go within one metre of any insect repellent.The minimum distance in metres the ant must traverse to reach the sugar particle is
(a) 3*square root of(2)
(b) 1+pie
(c)4*(pie)/3
(d) 5

Answer 1

the answer is C
if only one insect is standing in the middle,
the ant should walk on half the circumference of a circle with a radius 1 m to avoid the insect.
but there are 2 insects , so the 1m radius, 2 circles of them will intersect in a point x
BC =1 meter, BX = CX = 1meter (circle radius)
so this triangle will have all its angles equal 60
so the ant will have to walk 2/3 of the first circle circumference then another 2/3 of the second circle circumference .
= 2/3 (2 Pi (1)) + 2/3 (2 Pi (1)) = 4/3 pi = answer C

Answer 2

The area which is Within 1 m of the points B and C are both circles. He must travel 90 degrees of the circumference of the circle B, walk to circle C in a line parallel to AD, and a quarter of circle C.

the total is
2 pi r/4 + BC + 2 pi r/4
= 2 pi(1)/4 + 1 + 2 pi(1)/4
= pi/2 + 1 + pi/2
= 2pi/2 + 1
= 1 + pi

^_^

Answer 3

Two 90 degree arcs of radius 1, pi, plus a line segment of length 1 yields the answer 1 + pi, or (b).

Answer 4

3*sq rt(2)

Answer 5

d

Answer 6

Somebody's cheating on their homework....