Question

prove the following ​

Answer 1

Here we have to prove ∆APD ~ ∆CPB.

So,

angle APD = angle CPB

[ Vertically opposite angles]

angle DAP = angle PCB

[ AD \\ BC so, alternate intererior angles]

So,

∆ APD ~ ∆ CPB [ By AA similarity criteria]

Therefore,

AP/PC = PD/BP

AP×BP = PD×PC

AP/PD = PC/BP

Hence proved.