Let ABCD be a cyclic quadrilateral with AB = 15, BC = 20, CD = 24 and AC = 25. Then AD equals_________

Cyclic quadrilateral ABCD with $$AB = 15$$, $$BC = 20$$, $$CD = 24$$, $$AC = 25$$. In $$\triangle ABC$$: $$AB^2 + BC^2 = 225 + 400 = 625 = AC^2$$, so $$\angle ABC = 90°$$. Since ABCD is cyclic, $$\angle ADC = 90°$$ as well.

In $$\triangle ACD$$ (right-angled at D): $$AD^2 + CD^2 = AC^2 \Rightarrow AD^2 = 625 - 576 = 49 \Rightarrow AD = 7$$.