Question

if you are given, Chords and intersect at P. how would you prove AP·PC = BP · PD

Answer 1

heres the diagram https://acvirtual.owschools.com/media/g_geo_ccss_2015/7/group158.gif

Answer 2

join the ends of the chords and use a similar triangles

you have vertically opposite angles at P

you also have equal angles standing on the same arc are equal...

so the similarity proof in Angle Angle...

sides in the same ratio....

look at triangles APD and triangle BPC