Question

AB and CD are two parallel chords of a circle with centre O. AB = 8 cm and CD = 6 cm. If the distance between the chords is 7 cm, find the radius of the circle. AB and CD lie on the opposite sides of the centre.​

Answer 1

Answer:

Given

Δ ANO is a right angle triangle,

∴ using pythogoras theorem,

OA

2

=ON

2

+AN

2

13

2

=ON

2

+12

2

ON

2

=13

2

−12

2

=169−144

ON

2

=25

⇒ON

2

=5cm

Similarly for ΔOCM

OC

2

=OM

2

+CM

2

13

2

=OM

2

+5

2

OM

2

=13

2

−5

2

OM

2

=169−25

OM=

144

=12cm

∴ Distance between chords

=OM+ON

=12+5

=17cm.

Thus the distance between the two chords is 17cm.

Step-by-step explanation:

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