Question

PQRS is a cyclic quadrilateral in which PQ = x cm, QR = 16.8CM, RS = 14 cm, PS = 25.2 cm, and PR bisects

QS. What is the value of x?​

Answer 1

•Given :-

PQRS is a cyclic quadrilateral in which PQ = x cm, QR = 16.8CM, RS = 14 cm, PS = 25.2 cm, and PR bisects

•To find:-

the value of x

• Solution:-

As PR bisects

OQ= y and OS = y

as angle SPR = ϴ1 and angle SQR = ϴ1

and angle RSQ = ϴ2 and angle RPQ = ϴ2

and POS = QOR

from ∆PSO and ∆RQO

PQ/RS = OQ/OR

PQ/14 = y/OR....(1)

And from

∆POQ nad ∆ROS

y/OR = PS/QR = 25.2/16.8   ....(2)

From (1) and (2)

or,PQ/14= 25.2/16.8

or,PQ= 21 cm

so X is 21 cm