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

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Given: ` PD bot m`
`angle PDB = angle PDC = 90^*`
To Prove:` PB=PC`
Proof: In ` triangle PBD and triangle PDC`
`BD=DC` (given)
`PD=PD` (common)
`anglePDB=anglePDC=90^@`
`trianglePBD~=trianglePDC`(by SAS )
Hence Proved, PB=PC(By CPCT)
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