Question

If two equal chords PQ and RS of a circle
intersect at point T, then prove that PT = ST and
RT = QT.

Answer 1

Answer:

Since ,MN and RS intersect each other externally at point P

⇒PS×PR=PM×PN

PM=PN+MN

PN=3cm and MN=5cm

∴PM=3+5=8cm

And PS=PR+SR

PR=2 cm and SR=x cm

∴PS=x+2

⇒(x+2)×2=8×3

⇒2x+4=24

⇒2x=24−4

⇒2x=20

⇒x=

2

20

=10cm

∴SR=10cm