Question

$AB$ and $CD$ are two parallel chords of a circle of length $10cm$ and $4cm$ respectively. If chords lie on the same side of the centre and the distance between them is $3cm$, find the diameter of the circle.

Answer 1

According to the problem

$OA+OC$=radii of corcle

Therefore

$OE\perp AB,OC\perp CD$

Since

$AE=EB=5$Cm

$CF=FD=2$Cm

let $OE=X$Cm

In $\Delta OAE$,

$O{A}^2=A{E}^2+O{E}^2$

Implies that

$O{A}^2=5^2+x^2$ (1)

$In\Delta OCE,$

$O{C}^2=2^2+(x+3{)}^2$ (2)

Since

$5^2+x^2=2^2+(x+3{)}^2$

Implies that

$25+x^2=4+x^2+6x+9$

Implies that

$6x=25-13$

$6x=12$

$x=\frac{12}{6}$

$x=2$cm