Question # Two chords ( A B ) and ( C D ) of a circle intersect at ( E ) such that ( A E=2.4 mathrm{cm} ., mathrm{BE}=3.2 mathrm{cm} ) and ( mathrm{CE}=1.6 mathrm{cm} . ) The length of ( mathrm{DE} )

# Two chords ( A B ) and ( C D ) of a circle intersect at ( E ) such that ( A E=2.4 mathrm{cm} ., mathrm{BE}=3.2 mathrm{cm} ) and ( mathrm{CE}=1.6 mathrm{cm} . ) The length of ( mathrm{DE} )

is

(a) ( 1.6 mathrm{cm} )

(b) ( 3.2 mathrm{cm} )

(c) ( 4.8 mathrm{cm} )

(d) ( 6.4 mathrm{cm} )

Solution

(c) Apply the rule, ( A E times E B=C E times E D ) ( Rightarrow quad 2.4 times 3.2=1.6 times mathrm{ED} )

( therefore quad E D=4.8 mathrm{cm} )