Question

If two equal chords of a circle intersect within the circle, prove that the segments ofone chord are equal to corresponding segments of the other chord.

Answer 1

`AL= LB & CM = MD `
`AB _|_ OL and CD _|_ OM`
In `/_ LOX and /_ MOX`
`AB= CD & OL= OM`
`/_ OLX = /_ OMX = 90^O`
`OX= OX `common side in both triangles
`/_ LOX ~= /_ MOX`
`LX= MX` eqn(1)
`AB=CD` eqn (3)
`AB/2 = CD/2`
`So, BL= CM` eqn(2)
add eqn 1 & 2
`LX + BL = MX + CM`
`BX = CX` eqn (4)
subtract eqn 4 from 3 `AB - BX = CD- CX`
`AX= DX`hence proved