A regular hexagon is drawn with its vertices on a circle. Without looking into the picture, if one put dot in that picture, what is the probability of being the dot not in the regular hexagon?
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Answer:
The regular hexagon is inscribed in a circle of radius r.
So, it is inside the circle.
By joining opposite sides of hexagon, it forms 6 central angles at centre O each of which =
6
360
=60
o
.
And the six triangles are formed.
The two sides of each triangle are the radius of the circle and thus are equal., ∴ The base angles of every triangle are equal.
∵ Central angle is 60
o
⟹ Base angles =120/2=60
o
∴ The triangles are equilateral triangles.
⟹ All sides are equal.
∴ All sides of each triangle is r
Perimeter of regular hexagon =6×side=6r
Hence, option B is correct.
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