Anti frost faucet leak
From your side view it looks like there may be a minor leak around the valve stem just behind the faucet handle. You can investigate this by first removing the faucet handle. Then loosen and remove the part pointed to below:



(Do this with the faucet initially shut OFF).

Under this part you should find a rubber type part that fits around the valve stem. When this part is screwed in tighter it will compress the rubber part around the valve stem to keep it from leaking. 

Sometimes with age this rubber type part will get hard or cracked so that it can no longer provide a good seal against the valve stem. In this case it is necessary to replace the rubber part. 

There are also cases where the valve stem itself can get oxidized and/or corroded to the point that it no longer presents a nice smooth surface to the rubber seal part. It may be necessary to shine up the valve stem using a fine grade of steel wool. 

Sometimes it can be beneficial to lubricate the valve stem and inner surface of the rubber type seal part using some petroleum jelly.