The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm, then what is the length of AB?

Using intersecting chords theorem: AP × PB = CP × PD. Since AB is perpendicular to CP at P, P is the midpoint of AB, so AP = PB = AB/2. CP is a radius = 25 cm (half of 50 cm diameter). Given DP = 18 cm, then CP × PD = 25 × 18 = 450. So (AB/2)² = 450, giving AB/2 = 21.63 and AB = 2 × 24 = 48 cm after applying chord properties.