Question

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

Answer 1

According to the problem

OA+OC=radii of corcle

Therefore

OE⊥AB,OC⊥CD

Since

AE=EB=5Cm

CF=FD=2Cm

let OE=XCm

In ΔOAE,

OA

2

=AE

2

+OE

2

Implies that

OA

2

=5

2

+x

2

(1)

InΔOCE,

OC

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=

6

12

x=2cm