Question

if AB and CD are two chords of a circle we draw OE perpendicular to OF shuch that OE=OF than prove that AB equal to CD​

Answer 1

ǫᴜᴇsᴛɪᴏɴ →

if AB and CD are two chords of a circle we draw OE perpendicular to OF shuch that OE=OF than prove that AB equal to CD

ᴀɴsᴡᴇʀ →

By intersecting secant theorem,

PA×PB = PD×PC

8cm×3cm = PD×(PD+CD)

24cm

2= PD × (PD+2)

PD2 + 2PD − 24=0

On Solving the above quadratic equation, we get

PD2+6PD−4PD−24=0

(PD+6)×(PD−4)=0

PD=4cm & −6cm

So, PD=4cm is the real solution