Problem: Draw a chord in a circle with radius $5$ that subtends a central angle of $60^{\circ}$.\n\n1. Given.\nGiven a circle with center $O$ and radius $r=5$.\nWe want the chord that subtends central angle $\theta=60^{\circ}$.\n\n2. Construction steps.\nDraw the circle with center $O$ and radius $5$.\nChoose a point $A$ on the circle.\nConstruct the central angle $\angle AOB$ of $60^{\circ}$ to locate point $B$ on the circle.\nDraw the line segment $\overline{AB}$; this segment is the desired chord.\n\n3. Compute the chord length.\nUse the chord-length formula $c=2r\sin\left(\frac{\theta}{2}\right)$.\nSubstitute $r=5$ and $\theta=60^{\circ}$.\nCompute $\theta/2=30^{\circ}$.\nCompute $\sin(30^{\circ})=\frac{1}{2}$.\nTherefore $c=2\cdot 5\cdot \frac{1}{2}=5$.\n\n4. Check and interpretation.\nThe chord length equals $5$, which matches the side length of equilateral triangle $\triangle AOB$ formed when the central angle is $60^{\circ}$.\nThis provides both a synthetic construction and an algebraic verification.\n\nFinal answer: The chord length is $5$ and $\overline{AB}$ constructed above is the chord.\n