Question

Prove that out of two chords of a circle, the one which is closer to the centre is larger in length.
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Answer 1

Step-by-step explanation:

let C and c be two parallel chords in a circle.

on joining the ends of both chords to the centre, both chords forms a triangle,

let T be triangle formed by C

and t be triangle formed by c

• from figure it is clear that length of arc(L) by C is greater than length of arc(l).

therefore by formula:-

length of arc= angle by chord at centre × radius

L=(theta)×r

L directly proportional to theta a

also similarly,

l directly proportional to alpha

where theta>alpha.

therefore.. L>l

• mathematically length of arc is also directly to length of its chord

thus of L>l

this implies...

C>c.