Question

ABC and DBC are two right triangles with common hypotenuse BC and with their sides, AC and DB intersecting at P. Prove that AP. PC = BP . PD.

Answer 1

∴ ∠BAC = ∠BDC (each = 1 rt. ∠) 

∴ Pts. B, A, D, C are concyclic (∠s on the same side of segment BC are equal) 

∴ AP . PC = BP . PD (product of segments of intersecting chords of a circle)