Chord AB and diameter CD of a circle meet at the point P, outside the circle when the produced, If PB = 8 cm, AB = 12 cm and distance of P from the centre of the circle is 18 cm, the radius (in cm) of the circle is closest to

Using power of a point: When two chords intersect outside a circle, PA × PB = PC × PD. Given PB = 8, AB = 12, so PA = 20. Let radius = r, distance from center P to circle edge = 18. The power of point P = PT^2 = PO^2 - r^2 = 18^2 - r^2. Also, PA × PB = 20 × 8 = 160. So 324 - r^2 = 160, giving r^2 = 164, r = 12.806 cm ≈ 12.8 cm.