Answer: BD = 15 cm, BX = 9.6 cm
In right Δ BAD (∠A = 90º): BD² = AB² + AD² = 144 + 81 = 225, so BD = 15 cm.
∠AXD is an angle inscribed in a semicircle, so ∠AXD = 90º, i.e. AX ⊥ BD.
In right Δ BAD, AX is the perpendicular from the right angle to the hypotenuse, so Δ BXA ~ Δ BAD and AB² = BX × BD.
BX = \(\dfrac{AB^2}{BD} = \dfrac{144}{15}\) = 9.6 cm.