PQRS 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 & explanation
Correct answer: option 2
We know that , Angles made by an chord on the circumference of a circle are same.
Angles made by chord SP
⇒ ∠SQP = ∠SRO = ∠OQP
Similarly , Angles made by chord QR
⇒ ∠QPR = ∠QSR = ∠OSR
In triangle POQ and SOR,
∠POQ = ∠SOR
∠OQP = ∠SRO
∠QPR = ∠OSR
⇒ Triangle POQ ∼ SOR
We know that ,
\(\frac{OQ}{OR}\) = \(\frac{PQ}{SR}\)
( Gievn :- PQ = x cm )
\(\frac{OQ}{OR}\) = \(\frac{x}{14}\)
It is gievn that OQ = OS
⇒ \(\frac{OS}{OR}\) = \(\frac{x}{14}\) -----(1)
Similarly triangle POS ∼ QOR
\(\frac{OS}{OR}\) = \(\frac{PS}{QR}\)
\(\frac{OS}{OR}\) = \(\frac{25.2}{16.8}\) ----(2)
On comparing equation 1 and 2
\(\frac{x}{14}\) = \(\frac{25.2}{16.8}\)
x = \(\frac{25.2}{16.8}\) x 14
= 21 cm