Geometrical probability (part 1)

Geometry Level 3

Two points $A$ and $B$ are randomly selected from the circumference of a circle with centre $O$ and radius 1 cm. Find the probability that the length of chord $AB$ is greater than 1 cm.

Part 2 .

Part 3 .

\frac{1}{3}

\frac{1}{4}

\frac{5}{6}

\frac{1}{6}

\frac{2}{3}

\frac{1}{2}

\frac{3}{4}

1 solution

Chan Lye Lee
Oct 30, 2017

Note that the first point $A$ on the circumference can be any point. Construct a regular hexagon of side length $OA=1$ and the point $A$ is one of the the vertices. Refer to thee diagram below.

In order to have the length of chord $AB$ greater than 1, we need only to choose any point on the circumference except those coloured blue. This means that the probability is $\frac{2}{3}$ .

Geometrical probability (part 1)

1 solution

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