ABCD is a cyclic quadrilateral in which AB = 16.5 cm, BC = x cm, CD = 11 cm, AD = 19.8 cm, and BD is bisected by AC at O. What is the value of x ?
Answer & explanation
Correct answer: option 3
\(\angle\)ACD = \(\angle\)ABD (As Angle made by a chord in same segment are equal)
\(\angle\)BDC = \(\angle\)BAC (As Angle made by a chord in same segment are equal)
So, \(\Delta \)AOB is similar to \(\Delta \)DOC by AA.
\(\frac{AB}{DC}\) = \(\frac{OB}{OC}\)
= \(\frac{OB}{OC}\) = \(\frac{16.5}{11}\)
Given, OB = OD
\(\frac{OD}{OC}\) = \(\frac{16.5}{11}\) ..(1)
As we know,
\(\Delta \)ADO is similar to \(\Delta \)BCO
\(\frac{OD}{OC}\) = \(\frac{AD}{BC}\)
= \(\frac{OD}{OC}\) = \(\frac{19.8}{X}\) ..(2)
From eq (1) and eq (2)
\(\frac{19.8}{X}\) = \(\frac{16.5}{11}\)
= X = \(\frac{11\;×\;19.8}{16.5}\)
= X = 13.2 cm.