Question

P,Q,R and S are concyclic. PR bisects QS.if PQ=9 snd QR=8,RS=6 THEN PS=?​

Answer 1

Answer:

PS = 12

Step-by-step explanation:

In the given figure

∵ PR bisects QS

∴ OQ = OS

In ΔOPQ and ΔOSR

∠OPQ = ∠OSR   (angles in the same segment of circle)

Similarly

∠OQP = ∠ORS

∴ ΔOPQ ~ ΔOSR        (AA similarity criterion)

∴ PQ/SR = OP/OS       (corresponding sides of similar triangles are proportional)

∴ 9/6 = OP/OQ         (∵ OP = OQ)

⇒ OP/OQ = 3/2

In ΔOPS and ΔOQR

∠OPS = ∠OQR   (angles in the same segment of circle)

And ∠OSP = ∠ORQ   (angles in the same segment of circle)

∴ ΔOPS ~ ΔOQR        (AA similarity criterion)

∴ PS/QR = OP/OQ

⇒ PS/QR = 3/2

⇒ PS/8 = 3/2

⇒ PS = (3/2) × 8 = 12

Answer 2

Answer:12

Step-by-step explanation:

according to the property: PQ×QR = RS×PS

                                       ⇒  9 × 8 = 6 × PS

                                       ⇒  PS = (9 × 8) ÷ 6

                                        ∴  PS = 12