Question

In the figure, the chords AB and CD when produced-meet at P.PA=4cm,AB=8cm , CD = 2 cm , find PC.​

Answer 1

By intersecting secant theorem,

PA×PB = PD×PC

8cm×3cm = PD×(PD+CD)

24cm  

2

 = PD×(PD+2)

PD  

2

 +2PD−24=0

On Solving the above quadratic equation, we get

PD  

2

+6PD−4PD−24=0

(PD+6)×(PD−4)=0

PD=4cm & −6cm

So, PD=4cm is the real solution

Hope this helps!!! Thanks ❤️. Have a great day ahead. :D