What is the distance between two parallel tangents of a circle having radius 4.5 cm ?. Justify your answer.

Answer

Distance between parallel tangents is 9 cm.

Explanation

Let the centre of the circle be O. Let the tangents AB and CD touch the circle at points M and N respectively.
Draw seg OM and seg ON.
Through O, draw line XY || line AB
Line AB || line CD `" ""……."(" Given ")`
Line XY || line AB `" ""........"(" Construction ")`
`:.` line AB || line XY || line CD`" "".......(i)"`
`/_OMA=/_ONC=90^(@)" ""........"(" Tangent theorem ")`
Line AB|| line XY and line MO is the transversal,
`/_AMO+/_MOX=180^(@)" ""........"(" Interior angles theotem ")`
`:.90^(@)+/_MOX=180^(@)`
`:./_MOX=180^(@)-90^(@)`
`:. /_MOX=90^(@)`
Similarly `/_NOX=90^(@)`
`:./_MOX+/_NOX=90^(@)+90^(@)=180^(@)`
`:./_MOX " and " /_NOX` are adjacent as well as supplementary.
`:./_MOX " and " /_NOX` form linear pair.
`:.` ray OM and ray ON are opposite rays.
`:.` points M, O and N are collinear.
`:. MN` is the distance between the parallel tangents AB and CD
`MN= 2xx " radius "" " "......."(" Diameter is twice the radius ")`
`:.MN=2xx 4.5`
`:.MN=9` cm.