Question

If an arc of radius `6`cm subtends `60^@`, then what is the length of a chord joining its two ends?

Answer 1

The arc is `2pi` cm long.

Explanation:

The angle is one sixth of the complete `360°` angle, so the arc must be one sixth of the whole circumference. Since the radius is `6` cm, then the circumference is `2*6*pi` cm, which is `12pi` cm.

Dividing this quantity by `6`, we get `2\pi`, which is the requested value.

Answer 2

The chord is `6`cm long, since it is the side of a regular hexagon.

Explanation:

`6 xx 60^@ = 360^@` so the arc subtends the same angle as one side of a regular hexagon.

The hexagon can be dissected into `6` equilateral triangles with sides of length `6`cm which meet at the centre of the hexagon.