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

Step-by-step 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.