PQRS is a cyclic quadrilateral in which PQ = 14.4 cm, QR = 12.8 cm and SR = 9.6 cm. If PR bisects QS, what is the length of PS?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 19.2 cm.
Here,
ΔSOP is similar to ΔROQ [AAA property]
ΔSOR is similar to ΔPOQ [AAA property]
So,
(14.4/9.6) = (OQ/OR) ...............(1)
(OS/OR) = (PS/12.8)
[Given: OS = OQ]
So,
(OQ/OR) = (PS/12.8) -------------- (2)
From equation (1) and (2):
(14.4/9.6) = (PS/12.8)
⇒ 3/2 = (PS/12.8)
⇒ PS = (3/2) × 12.8
⇒ PS = 19.2 cm