Question
Download Solution PDFPQRS is a cyclic quadrilateral in which PQ = x cm, QR = 16.8 cm, RS = 14 cm, PS = 25.2 cm, and PR bisects QS. What is the value of x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
From the following figure
∠SQP = ∠OQP = ∠SRO
OQ = OS (Given)
∠QPR = ∠QSR = ∠OSR
∴ We can say that,
ΔPOQ∼ΔSOR
PQ/SR = OQ/OR
OQ/OR = x/14
Given, OQ = OS
OS/OR = x/14 --- (1)
As we know,
ΔPOS∼ΔQOR
OS/OR = PS/QR
OS/OR = 25.2/16.8 --- (2)
From equation (1) and equation (2)
x/14 = 25.2/16.8
x = (25.2 × 14)/16.8
∴ x = 21 cm
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