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Of all the line segments drawn from a point `P` to `a` line `m` not containing `P ,` let `P D` be the shortest. If `B` and `C` are points on `m` such that `D` is the mid-point of `B C` , prove that `P B=P Cdot`

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24114 `PB` is the shortest
Therefore `PDbotM`
`anglePDB=anglePDC=90^0`
In `trianglePDB` and `trianglePCD`
`PD=PD`....(common)
`trianglePDB=trianglePDC`.................(By `angle 90^0`)
`BD=DC` (given)
Therefore `trianglePDB cong trianglePDC`.........(SAS)
By CPCT
`PB=PC`
Hence the proved.
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