Question

AB and CD are two chords of a circle on the same

side of the centre such that AB = 8 cm, CD = 10 cm

and AB || CD. If the distance between AB and CD

is 2 cm, then find the radius of the circle.​

Answer 1

Answer:

17cm

Step-by-step explanation:

Given

Δ ANO is a right angle triangle,

∴ using pythogoras theorem,

OA2 =ON2  + AN2

(13)2 = ON2 + (12)2

ON2 = 13^2 - 12^2

       =  169 - 144

        = 25

ON= $\sqrt 25$ = 5cm

Similarly for ΔOCM

OC^2 = OM^2 + CM^2

13^2 = OM^2 + 5^2  

OM^2= 13^2 - 5^2

        =  169 - 25

        = 144

OM = $\sqrt144$ = 12cm

∴ Distance between chords

=OM+ON  

=12+5

=17cm.

Thus the distance between the two chords is 17cm.

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