Two chords AB and CD of a circle intersect each other at a point E outside the circle. If `AB= 11 cm, BE = 3cm ` and `DE = 3.5cm`, then `CD = ?`

Options

A. 10.5 cm
B. 9.5 cm
C. 8.5 cm
D. 7.5 cm

Answer

C

Explanation

Join AC . Then,
`AE: CE = DE : BE`
`:. AE xx BE = CE xxDE`
Let CD `= x cm `. Then,
`AE = (AB+ BE) = ( 11+3) cm = 14 cm, BE = 3 cm, CE = ( x + 3.5 ) cm ` and `DE = 3.5 cm`
`:. 14 xx 3 = ( x+ .3.5) implies x + 3.5 = (14 xx 3)/( 3.5) = 12`
`implies x = (12 - 3.5 ) = 8.5 cm`
`:. CD = 8.5 cm`