Question

Question #f919f

Answer 1

The length of a chord is `4` (answer #2)

Explanation:

Consider a Cartesian coordinate system on a plane with origin `O`, axis `OX` (abscissa) and axis `OY` (ordinate).

A circle defined by equation `x^2+y^2=16` has a radius `R=sqrt(16)=4` and a center at origin `O`.

Point `A=(4cos theta, 4sin theta)` lies on this circle such that angle `/_XOA=theta` (counterclockwise from axis `OX` to radius `OA`)

Point `B=(4cos(theta+60^o), 4sin(theta+60^o))` also lies on this circle making an angle between X-axis and radius `OB` larger than `/_XOA` by `60^o` counterclockwise.
So, `/_XOB=/_XOA+60^o`

Therefore, the angle between radiuses `OA` and `OB` is `/_AOB=60^o`

Now it is obvious that triangle `Delta AOB` is equilateral since `OA=OB` as radiuses and `/_AOB=60^o`.

Therefore, `AB=OA=OB=4`.