At one end P of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn. The length of the chord RS parallel to XY and at a distance of 8 cm from P is :

The circle has radius 5, so the diameter is 10. The chord RS is parallel to the tangent at P, meaning it is perpendicular to the diameter. The distance from P to the chord is 8. The distance from the center to the chord is |8 - 5| = 3. Using the Pythagorean theorem on the triangle formed by the radius, the distance to the chord, and half the chord length: (half-chord)^2 + 3^2 = 5^2. (half-chord)^2 = 25 - 9 = 16. Half-chord = 4. Total chord length = 8.