Question

A circle with center 0 and radius 5 has a central angle X O Y . If m ˆ X Y = 60 ∘ , what is the length of chord X Y ? Round your answer to the nearest whole number.

Answer 1

Answer: 5

Explanation:

As all radii of a circle are congruent,
`\overline{OX} \cong \overline{OY}`, it follows that
`\angle OXY \cong \angle OYX`.

Because arc XY measures 60 degrees, we also know that
`m\angle XOY=60^(\circ)`, and thus triangle OXY is equilateral.

Hence, XY=5 because all sides of an equilateral triangle are congruent.