In the given figure, `AB` and `CD` are two parallel chords of a circle with centre `O` and radius 5cm such that `AB = 8` cm and `CD = 6` cm. If `OP` `_|_` `AB` and `OQ` `_|_` `CD`, determine the length `PQ.`

Explanation

We know that the perpendicular from the centre of a circle to a chord bisects the chord.
`:. AP = (1)/(2)AB=((1)/(2)xx8)cm=4cm`.
`CQ =(1)/(2)CD =((1)/(2)xx6)cm=3cm`
Join `OA` and `OC.`
Then, `OA` `=` `OC` `=` `5 cm.`
From the right -angles `Delta OPA` , we have
`OP^(2)=OA^(2)-AP^(2)= [(5)^(2)-(4)^(2)]cm^(2)=9cm^(2)`
`impliesOP = 3cm`.
From the right angled `Delta OQC`, we have
`OQ^(2)=OC^(2)-CQ^(2)= [(5)^(2)-(3)^(2)]cm^(2)=16cm^(2)`
`implies OQ=4cm`
Since `OP` `_|_` `AB`, `OQ ` `_|_` `CD` and `AB` `||` `CD`, the points `P,O,Q` are collinear
`:. PQ = OP +O =(3+4)cm=7cm`