Question

prove that if any two chords of a circle are drawn than the one which is nearer to the centre is larger​

Answer 1

Step-by-step explanation:

Let r be the radius of the circle.

Given a chord, let c be half its length (so it is 2c long) and let d be its distance from the centre of the circle.

We have a right angled triangle with a radius, half the chord and the partial radius from the centre to the midpoint of the chord.

By Pythagoras' Theorem,

c² = r² - d².

So the nearer the chord is to the centre, the smaller is d, the smaller is d², the larger is c², the larger is c, and so the larger is the chord.